This paper presents a modified predictive current control (PCC) algorithm for five phase permanent magnet motor with non-sinusoidal back electromotive force (back-EMF), which reduces torque ripples and computational burden significantly. A cost function based on voltage tracking errors is proposed. One active voltage vector in combination with one zero voltage vector are applied to the inverter each sampling period. The switching instant is calculated analytically by solving a minimization problem of the cost function. The proposed cost function is evaluated 6 times each sampling period, thus the computational burden is greatly reduced. Simulation results show that torque ripples are greatly reduced and the currents are less distorted by using the proposed method.