A doubly clad optical fiber with an inner cladding made of a uniaxial crystal material whose optical axis is parallel to the fiber axis was proposed, and exact characteristic equations of vector modes were derived. The influence of the ratio (kcl) of the extraordinary to the ordinary ray indexes upon the waveguide dispersion was examined in detail. In view of the impossibility to deduce the expression of waveguide dispersion directly due to the complexity of the characteristic equations, a feasible approach to calculate waveguide dispersion was established. The calculated results indicate that the values of waveguide dispersion can be effectively changed through variation of kcl without changing the geometrical and optical parameters (S and R). The influences of kcl, S and R on the propagation and cutoff characteristics of the low order modes are also analyzed.