Heads up for a wall of text 
You have to look at the whole picture to understand where control valve (or any pressure letdown elements) come into play in hydraulics.
Normally, you'd have a source (with fixed pressure P1) and a destination (fixed pressure P2) connected by a pipe with a control valve on it (or an ordinary valve for that matter).
If the valve is closed, then no flow goes through with it and the pressure upstream and downstream of the valve would be P1 and P2, respectively.
When you start opening up a valve, there would be a path where a flow from a higher pressure (P1) to a lower pressure (P2) can occur, and in fact, flow must occur. The amount of flow will depend on these:
1. Pressure loss upstream of valve
2. Pressure loss downstream of valve
3. Pressure loss across the valve itself.
And the summation of the pressure losses (sumDelF) above must match the pressure differential (P2-P1, assuming no static head exists for the benefit of discussion).
I think it's safe to say that for the vast majority of hydraulics, pressure loss at #3 is controlling, but it doesn't mean that losses from #1 and #2 can be ignored.
As you open the valve further, less constriction occurs on the valve, so more flow has to be allowed. Still, sumDelF=P2-P1 has to be satisfied at all times, so the reduction of pressure drop in #3 has to be accounted for. And it will be accounted for by an increase in pressure drop for both #1 and #2 (because pressure drop is proportional to increase in flow).
So to answer your question:
For a control valve I know that when the opening increase, flowrate also increase in actual.
This is true, provided that the pressure at inlet and outlet of valve remains the same.
When valve opening increases, the pressure drop across it should reduce. And when the pressure drop across it is reduced then it should lead to a decrease in flowrate since the pressure drop across the valve drives the flow. This is counter-intuitive to what I said earlier which should give rise to an increase in flowrate.
You have to realize that what you only did when you open a valve is to have a larger area for a flow to go through. The flow across the valve still depends on how much upstream and downstream pressure you have on your valve.
Since you have a bigger area for flow to pass through, it follows that you'd have more flow on your valve (less resistance to flow). While it's tempting to assume that the pressures upstream and downstream would be P1 and P2 respectively, we also have to account for the pressure losses on your piping, which in turn depends on flow.
So there should be a point where all balances out, when for a given flow F, the pressure losses for both upstream and downstream piping will result in an upstream (P1-delPupstream) and downstream pressure (P2+delPdownstream) that will in turn, results in the same flow F for a given valve opening (constriction).
As pointed by the other members here, valve opening represents resistance to flow. Just think of a valve opening as a length of pipe (with a given diameter). When it's opened 100%, the length is at a minimum. As you close the valve, this length increases and it goes into infinity as you close it fully. It might not be a good analogy but I hope you get the drift.
However with mansuri's explanation, for a fixed dP system increase in the control valve opening will result in more flow. In that case since the dP across the whole system is fixed, I don't see how increasing or decreasing the control valve can affect the flowrate according to theory, since the flow should be the same with the same dP across the system, irregardless of the opening of the control valve.
While your system dP (P2-P1) is fixed, the resistance to flow is not, at least for the valve. Closing the valve is akin to increasing the flow resistance so by closing the valve, you'd have less flow (and it goes vice versa).