This article presents an efficient and effective modified generalized reflection and transmission (R/T) (mGRT) coefficient method for dispersion‐curve calculation of the Rayleigh and Love waves. We construct a novel dispersion function based on the kernel function for calculating synthetic seismograms in an elastic layered half‐space model. It improves the root searching using the monotonicity of the dispersion function in sections between roots. We introduce an auxiliary function to accelerate the root‐searching procedure by approximating the number of roots of the dispersion equation. To solve the low‐velocity‐layer problem for the generalized R/T coefficient method, we turn to the dispersion function of multiple depths. Numerical results indicate that the proposed method is slightly slower than the other most efficient methods including the delta‐matrix method and the fast delta‐matrix method. Then, we present a technique for the velocity and attenuation dispersion curves in viscoelastic media. The technique is based on jumping features of the dispersion function and converts 2D root‐searching problem to 1D minimization problem. The mGRT method is expected to be a useful candidate for calculating dispersion curves in both elastic and viscoelastic media.