A selective harmonic elimination pulse width modulation (SHEPWM) control strategy is proposed to balance the neutral-point potential (NP) of a three-level active neutral-point-clamped (ANPC) converter. In this strategy, the chaotic ant colony algorithm (ACA) is adopted to solve the SHEPWM nonlinear equations, which does not require presetting the initial values of solutions and can get multiple solutions in the same modulation index. The influence of different solutions corresponding to the SHEPWM switching states on the NP is different, namely, some make the NP increase and others make the NP decrease. Therefore, the NP balancing can be effectively controlled by choosing appropriate solutions in different fundamental periods. The simulation and experimental results further verify the feasibility and effectiveness of the control strategy.