In this paper, an improved approach of extended non-minimal state space (ENMSS) fractional order model predictive control (FMPC) is presented and tested on the temperature model of an industrial heating furnace. In the fractional order model predictive control algorithm, fractional order single-input single output (SISO) system is discretized via fractional order Grdnwald-Letnikov (GL) definition. The ENMSS fractional order model that contains the state variable and the fractional order output tracking error is formulated by choosing appropriate state variables. Meanwhile, the fractional order integral is introduced into the cost function and the GL definition is used to obtain the discrete form of the continuous cost function. Then the control signals are derived by minimizing the fractional order cost function. Lastly, the temperature process control of a heating furnace is illustrated to reflect the performance of the proposed FMPC method. Simulation results show the effectiveness of the proposed FMPC method. (C) 2017 Elsevier Ltd. All rights reserved.