Pedestrian inertial navigation is a pivotal technology for achieving seamless indoor and outdoor positioning. Traditional methods based on the Extended Kalman Filter (EKF) suffer from cumulative errors induced by inertial measurement unit (IMU) noise, which severely degrade the accuracy of pedestrian trajectory estimation over long durations. To address this critical limitation, a post-processing trajectory optimization approach for pedestrian inertial navigation based on the Birkhoff pseudospectral method is proposed in this paper. Leveraging the initial attitude and position estimates derived from the Zero-Velocity Update (ZUPT) technique and the EKF framework, the proposed method first parameterizes continuous-time acceleration measurements by adopting Chebyshev nodes as collocation points, and then formulates and solves the trajectory optimization problem via a Birkhoff pseudospectral framework, which effectively suppresses noise interference from the IMU accelerometer. Simulation experiments validate the superior noise suppression capability of the proposed algorithm. Furthermore, physical experiments conducted with a foot-mounted IMU demonstrate that the final position error is reduced by approximately 90% in comparison with the traditional EKF-based method.