A variant of the subdomain Galerkin method has been set up to find numerical solutions of the Burgers' equation. Approximate function consists of the combination of the trigonometric B-splines. Integration of Burgers' equation has been achived by aid of the subdomain Galerkin method based on the trigonometric B-splines as an approximate functions. The resulting first order ordinary differential system has been converted into an iterative algebraic equation by use of the Crank-Nicolson method at successive two time levels. The suggested algorithm is tested on some well-known problems for the Burgers' equation.