In indoor temperature control of a heat pump, a reduction in energy consumption is very important. However, most control schemes for heat pumps have focused only on control performance such s settling time and steady-state error. In this paper, the model predictive control (MPC) which includes the energy-related variable in this cost function is proposed. By computing the control signal minimizing this cost function, the trade-off between energy reduction and temperature control performance can be obtained. Since the MPC required the process model, the dynamic mode of a heat pump is also obtained by the system identification technique. Performance of the proposed MPC considering energy efficiency is compared with the two other control schemes. It si shown that the proposed scheme can consume less energy thant hte others in achieving similar control performance.