In the geometric shape design, shape preserving interpolation of curve/surface is an important and difficult subject in which both monotonicity-preserving and convexity-preserving interpolation are two basic contents. In this paper, the monotonicity-preserving interpolation of a kind of plane parameter curve with a shape control parameter is investigated. The basic idea is as follows: first, a kind of plane α-B-spline interpolation curve with a shape control parameter a is constructed; then, by converting the first derivatives of the curve into Bernstein polynomial, the positive conditions of Bernstein polynomial can be used to get the necessary and sufficie nt conditions for the monotonicity of α-B-spline interpolation curves, i.e., the range of the parameter a. Therefore, monotone-preserving interpolating curves can be obtained succinctly. Numerical examples illustrate the correctness and the validity of theoretical reasoning. In virtue of its convenience and efficiency, this method is hopeful to be widely applied to engineering and practice.