In the connection of two optical fibers, higher-order modes appear occasionally even for slight shift of the two fibers. In usual fiber, four higher-order modes, TE₀₁, TM₀₁ and two of HE₂₁ modes, have slightly different eigenvalues and field distributions of two-lobe patterns described by linearly polarized E_x and E_y, respectively. Then in order to investigate precisely the occurrence mechanism of such higher-order modes, accurate full-vectorial numerical method is required. In this paper, Fourier series expansion method is applied to the full-vectorial analysis of the connection problem. First, the eigenvalues and the field distributions of the four higher-order modes in step-index type optical fibers are computed by the method, and their accuracies are examined. Then the occurrence mechanism of the higher-order modes caused by the transverse shift of the two fibers is made clear.