Commercial Fixed Wing
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 70; Flight Crew Total 17480; Flight Crew Type 2094
Human-Machine Interface; Situational Awareness
Aircraft Equipment Problem Less Severe; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Issued New Clearance; Flight Crew Returned To Clearance; Flight Crew Overcame Equipment Problem
Procedure; Human Factors; Environment - Non Weather Related; Aircraft
Climbing we were assigned 10;000 feet at 7;000 FMA said ALT due to the fast climb and turbulence. Passing 8;000 feet ATC reassigned to level off at 9;000 feet; but airplane  was slow to capture ALT of 9;000 feet due to high climb rate and turbulence; moderate; and after passing 9;300 feet I disconnected the A/P and A/T and stopped climb at 9;600 feet and was correcting back to 9;000 feet when ATC noticed we had passed 9;000 feet and issued climb to 10;000 feet. ATC was step climbing us due to aircraft in front. No TA or RA or ATC immediate commands were generated. Due to moderate turbulence and high v/s climb I did not feel the need to over aggressively correct the altitude back to 9;000 feet and risk injuring a FA or passenger; knowing clearly that the step climb was due to traffic ahead we were outperforming. Flight continued safely and uneventfully.
We departed ZZZ on Runway XX climbing to 3;000 feet. The Departure Controller gave us a climb to 10;000 feet. The airplane was light 350;000 pounds and was climbing at over 3;000 FPM. Passing 7;000 feet the FMA changed to VNAV ALT to begin the level off at 10;000 feet. The Controller amended our altitude to 9;000 feet when we were passing about 7;500 feet. We input the 9;000 feet to the MCP but the Autopilot overshot 9;000 feet and I told the PF that the autopilot was not making the level off at 9;200 feet. We leveled off at 9;500 feet and started to correct to 9;000 feet. The Controller then told us to continue climb to 10;000 feet. We climbed to 10;000 feet and the rest of the flight was uneventful.
Air Carrier flight crew reported over shooting an altitude during departure.