A video stabilization algorithm based on feature tracking and mesh path motion is proposed to solve the jitter video issues for handheld mobile devices. The algorithm uses SIFT algorithm to extract the feature points of video frames, uses KLT algorithm to track the feature points, uses RANSAC algorithm to estimate the affine transformation matrix between adjacent frames, divides the video frames into uniform grids, calculates motion trajectories of the video, and then optimizes the smoothing of multiple mesh paths by minimizing the energy function. Finally, the compensation matrix between adjacent frames is calculated by the relationship between the original camera path and the smoothed camera path, and then each frame is geometrically transformed by the compensation matrix to obtain a stable video. Experiments show that the proposed algorithm has good results for the jitter video captured by handheld mobile devices. The average PSNR after image stabilization is approximately 11.2 dB higher than that of the original jitter video, and is approximately 2.3 dB higher than the bundled camera path method. The average structural similarity (SSIM) between images is increased by approximately 59%, and is approximately 3.3% higher than the bundled camera path method.