A semianalytic method to solve the multigroup transport equation is presented. Here, the collision source is represented as a piecewise continuous function in space, preserving its finite spatial moments. The angular flux is analytically evaluated. The performance of the method is compared with the DSN method in a problem of gamma-ray transport through a 1-m-thick block of iron. It is found that one can obtain accurate solutions with the present method using relatively coarse spatial cells, leading to a significant reduction in computing time.