According to the periodic extension fact for closed curve, a method of cubic B-spline interpolation for closed curve was proposed. By extending knots and control points, the interpolated curve closed entirely at closing point. Considering the character of incomplete bond matrix for coefficient matrix of interpolation system of equations, an algorithm for solving linear banded system of equations with two columns of non-zero elements was introduced to improve the computational efficiency. Examples of application show that the proposed technology has the stable performance and high efficiency, can be used to interpolate complex closed curve with whatever shape, and it is especially useful for problems with large number of data points.