I know that during a/c climb, rate of climb indicator is climb position.
But my pilot said that about 4minute after take off indcated decent posion.
Why do this situation?
You did not mention what type of aircraft. I am going to assume it is a pressurized jet aircraft and that when you say "rate of climb indicator" you are talking about the cabin pressure rate of climb indicator and not the aircraft vertical speed indicator.
What was the altitude of the departure airport; was it a high altitude airport say like Mexico City > 7,000? What was the altitude of the landing altitude, was it much lower than the departure elevation? What was the cruise altitude set in the digital pressurization controllers flight altitude? Not having the pressurization panel set up correctly can lead to "different" readings.
If you take off from a relatively high altitude airport with the intention of landing at a much lower altitude airport it may be normal for the rate of climb to indicate a descent after takeoff as the cabin controller is pressurizing for the scheduled differential and the landing altitude. When we depart out of Mexico City for a sea level airport several hours later the cabin will initially indicate a descent during the climb out phase.
The flight did not take off unpressurized and then airborne the packs selected on was it? If you take off unpressurized, for performance reasons, then select the packs on you will get the descend indication while the jet is climbing. Under that condition it would be a normal indication.
It is possible that your outflow valve is sticking and not responding to the inputs from the pressure controller(s).
When I depart a sea level airport and climb to altitude passing through 10,000’ the cabin altitude is at approximately thefirst index mark off zero well below 1,000’, passing through FL180 the cabin
differential is about 6 (If it were a clock it would “look” like 1:30 +/-). At FL350 the cabin should be around 7,000 +/-, there is a placard on the pressurization panel for reference. Did your jet pressurize on schedule?