Multiphase machines are characterized by high power density, enhanced fault-tolerant capacity, and low torque pulsation. For a voltage source inverter supplied multiphase machine, the probability of load imbalances becomes greater and unwanted low-order stator voltage harmonics occur. This paper deals with the PWM control of multiphase inverters under unbalanced load conditions and it proposes a novel near-five-vector SVPWM algorithm based on the five-phase six-leg inverter. The proposed algorithm can output symmetrical phase voltages under unbalanced load conditions, which is not possible for the conventional SVPWM algorithms based on the five-phase five-leg inverters. The cause of extra harmonics in the phase voltages is analyzed, and an xy coordinate system orthogonal to the ${alpha}{eta}z$ coordinate system is introduced to eliminate low-order harmonics in the output phase voltages. Moreover, the digital implementation of the near-five-vector SVPWM algorithm is discussed, and the optimal approach with reduced complexity and low execution time is elaborated. A comparison of the proposed algorithm and other existing PWM algorithms is provided, and the pros and cons of the proposed algorithm are concluded. Simulation and experimental results are also given. It is shown that the proposed algorithm works well under unbalanced load conditions. However, its maximum modulation index is reduced by 5.15% in the linear modulation region, and its algorithm complexity and memory requirement increase. The basic principle in this paper can be easily extended to other inverters with different phase numbers.