B-spline functions necessitate piecewise interval calculations under De Boor algorithm, while Legendre polynomials enable global domain operations without segmentation. This characteristic renders Legendre polynomials computationally more efficient. Motivated by this efficiency, we introduce Legendre-KAN, a reformulated version of Kolmogorov-Arnold Networks (KAN) that substitutes B-spline basis functions with Legendre polynomials. Our approach reparameterizes the network's weights using Legendre polynomials, which not only substantially reduces training time but also preserves competitive approximation accuracy, albeit with marginally higher root-mean-square error (RMSE) in certain tasks. Experimental results confirm that Legendre-KAN provides a computationally efficient alternative to traditional KAN architectures and surpasses MLP modules in terms of training accuracy. This work offers a promising avenue for addressing the inherent time-cost challenges in KAN.