In this paper, the Taylor series approximation approach is introduced in the analysis of bilinear systems. Despite the obnoxious properties of bilinear time-variant systems, the Taylor series approach may suitably solve it through the simple formation of the operational matrix of integration. The operation of a set of algebraic equations is greatly simplified just by taking a small number of terms. The result is in satisfactory agreement with the exact solution. An illustrative example is shown to support this method.