Air carrier captain reported an airborne conflict while climbing to assigned altitude.

Attributes
ACN	1765071
Time
Date	202010
Local Time Of Day	1801-2400
Place
Locale Reference	ZZZZ.ARTCC
State Reference	US
Environment
Flight Conditions	VMC
Aircraft 1
Make Model Name	Commercial Fixed Wing
Operating Under FAR Part	Part 121
Flight Phase	Climb
Flight Plan	IFR
Aircraft 2
Make Model Name	Any Unknown or Unlisted Aircraft Manufacturer
Flight Phase	Cruise
Flight Plan	IFR
Person 1
Function	Pilot Not Flying Captain
Qualification	Flight Crew Instrument Flight Crew Multiengine Flight Crew Air Transport Pilot (ATP)
Events
Anomaly	Conflict Airborne Conflict Deviation - Altitude Excursion From Assigned Altitude Deviation - Procedural Clearance

Narrative:

While climbing to FL360 ZZZ center told us we had traffic at our 1 o'clock heading toward us at FL370. We called the aircraft in sight and continued our climb to FL360. Passing FL352 we received a TA and my first officer went to engage vertical speed; but was unable since the autopilot already engaged altitude hold. Vertical speed indicator was decreasing nicely for level off at FL360. However; we then received a RA which directed us to level off. My first officer disengaged the autopilot and leveled off at FL357. Once we received clear of conflict we finished our climb to FL360 and notified ATC of RA. We never lost sight of aircraft nor exceeded FL360.light airplane; higher than normal vertical speed in climb; autopilot engaged altitude hold preventing first officer from going to vertical speed.even though aircraft was in sight and aircraft was leveling at assigned altitude we should have decreased the vertical speed to 1;000 FPM or less once inside 5 miles and 2;000 feet of conflict to prevent from getting a TA followed by a RA.

Original NASA ASRS Text

Title: Air carrier Captain reported an airborne conflict while climbing to assigned altitude.

Narrative: While climbing to FL360 ZZZ Center told us we had traffic at our 1 o'clock heading toward us at FL370. We called the aircraft in sight and continued our climb to FL360. Passing FL352 we received a TA and my FO went to engage Vertical Speed; but was unable since the autopilot already engaged altitude hold. Vertical speed indicator was decreasing nicely for level off at FL360. However; we then received a RA which directed us to level off. My FO disengaged the autopilot and leveled off at FL357. Once we received clear of conflict we finished our climb to FL360 and notified ATC of RA. We never lost sight of aircraft nor exceeded FL360.Light airplane; higher than normal vertical speed in climb; autopilot engaged altitude hold preventing FO from going to vertical speed.Even though aircraft was in sight and aircraft was leveling at assigned altitude we should have decreased the vertical speed to 1;000 FPM or less once inside 5 miles and 2;000 feet of conflict to prevent from getting a TA followed by a RA.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.