Two different types of few mode fibers (FMFs) are considered: a graded-core with a cladding FMF and a multi-step-index FMF. The characteristics of mode field distribution and the effective index are analyzed based on Comsol software. Then differential mode delay is analyzed. The structure and profile parameters are optimized in order to achieve the lowest possible differential mode delay (DMD). Under the condition of supporting four modes, a graded-core with a cladding FMF is designed. The DMD absolute values of LP11, LP21, LP02 are all below 0.015 ps·m-1. Under the condition of supporting two modes, a multi-step-index FMF is designed. The DMD of LP11 is 0.185 ps·m-1. The designed fibers have low DMD, which is suitable for mode division multiplexing.