The precise alignment of a high-performance telescope is a key factor to ensure the imaging quality. However, for telescopes with a wide field of view, the images are sometimes under-sampled. To study the effects of under-sampled images on the precision of telescope alignment, numerical simulations are implemented with the stochastic parallel gradient descent algorithm. The results show that the alignment program can converge stably and quickly. However, with the reduction of the full width at half-maximum of images, the relative residual errors increase from 9.5% to 19.5%, and the wavefront errors raise from 0.0972$\lambda$ to 0.1074$\lambda$, indicating that the accuracy of the alignment decreases.