On the basis of the improved algorithm for electromagnetic scattering of plane waves by multilayered spheres, a stable, efficient numerical algorithm to compute the scattering coefficients of a multilayered cylinder of infinite length is proposed. Compared with previous algorithms, the computation for scattering field in the proposed one is extended to fairly large parameters, up to 10000 and 106 in number of layers, and the operating time is not more than several seconds. The algorithm can also be used for absorbing or nonabsorbing cylinders of infinite length in different wavebands and different fields. At last, the algorithm is used in the study on scattering of gradient refractive-index polymer optical fiber, which supplies theoretical base for non-intrusive on-line measurement of refractive index by light scattering.