This paper presents the steady-state heating performance of a multi-type heat pump system. The compressor and expansion valves are described by a lumped parameter model for its rapid and prompt response to the disturbances compared to those of the heat exchangers. Fully distributed model (or spatially dependent model) is used for the evaporator and condenser since the lumped method does not guarantee enough accuracy in estimating the performance of heat exchangers with phase change. Most researches on the numerical simulation in heat pump system focuses on the precise modeling for the steady or transient states while few researches on the simulations consider the relationships among several indoor units, expansion valve openings and compressor speed in multi-type heat pump system. In this study, the heating performance of a multi-type heat pump system using R410A with three indoor units is simulated for the investigation of system characteristics and the simulation results are verified for several experimental conditions. Finally, the simulation technique is extended to the system with $n$-indoor units.