The solution of characteristic equation of multimode step-index fiber core conduction mode is involved in many cases, such as the mode dispersion solution of multimode fiber, the theory analysis of optical fiber coupled-mode, and the mode evolution of tapered fiber. The large computation capability of this solution affects the whole computational efficiency directly. The Newton-Raphson iteration method is analyzed and it has obvious advantage in convergence speed. In the solving process of scalar mode characteristic equation under the weak-guidance approximation, we use the zero point of the type I Bessel function to determine the interval of roots, then solve the characteristic equation quickly in the interval by combining the Newton-Raphson iteration method. The solving process is introduced in the solving of vector mode characteristic equation, and its first root and last root are determined quickly by combining the way of upper and lower boundary chord intercept. Finally, we compare the calculation results of our method with the results of OptiFiber software, draw the mode dispersion curve of fiber, and verify the accuracy of our method.