We have proposed a refractive index profile such that the first four LP modes (LP01, LP11, LP02 and LP21) propagate with the same group velocity through the optical fiber. Numerical method has also been proposed to compute the group delays of these modes. The refractive index profile has power-law index variation with more than one profile exponent within the core over different radial distances from the axis. Thus it is an intermodal dispersion free few-mode fiber as only four modes propagate. This may find application as transmission medium in optical telecommunication system as a larger core radius alternative to conventional single-mode fiber.