In this paper, we prove uniform Hausdorff and packing dimension results for the images of a large family of Markov processes. The main tools are the two covering principles in Xiao (In Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot, Part 2 (2004) 261-338 Amer. Math. Soc.). As applications, uniform Hausdorff and packing dimension results for certain classes of Levy processes, stable jump diffusions and non-symmetric stable-type processes are obtained.