More accurate analytical solutions of the maximum rate of climb and maximum climb angle are proposed for the climbing flight of the piston-propeller airplane. For the solutions, it is assumed that the propeller efficiency is a function of the airspeed and the airplane has cambered wing drag polar. The solutions are compared with the performance calculated through traditional assumptions of a constant propeller efficiency and a symmetrical wing drag polar. Moreover, the quartic equation to find the best climb angle speed is solved exactly. The comparison proved that the solutions with traditional assumptions result in a higher service ceiling, a shorter climb time, and a shorter climb distance.