Freedom curve/surface reconstruction with normal constraints is crucial in optical reflecting surface design. In this paper a binary code based genetic algorithm for knot optimization scheme is proposed to reconstruct a B-spline curve that not only approximates the data points but also meets the corresponding normal constraints. First, the constrained optimization problem is transformed into an unconstrained optimization problem by means of penalty function method. Then, the binary code based genetic algorithm (GA) is applied to find the best knot vector after establishing a suitable fitness function. Finally, adaptive generation of optimal knot vector and iterative evolution result in a satisfactory reconstructed curve. Since knot vector is non decreasing,and genetic algorithm may disrupt the order of knot vector in searching for the optimal knot vector, a process is also built to adjust variables into disordered bounded variables in the fitness function. Test results and a comparison with the traditional least square method as well as modern particle swarm optimization method show that the proposed scheme for reconstructing B-spline curve with normal constraints is superior and effective on arbitrary shape of discrete data set.