The homotopy analysis method is applied to seek periodic solutions of a nonlinear jerk equation involving the third-order time-derivative.The periodic solutions can be approximated via an analytical series.An auxiliary parameter is introduced to control the convergence region of the solution series.Two numerical examples are presented to demonstrate the effectiveness of the homotopy analysis approach.The examples indicate that.by choosing a proper value of the auxiliary parameter, the first few terms in the solution series yield excellent results.