In this work, the authors offer a novel and accurate method in order to find the solution of the linear differential equations over the intervals [0, 1) based on the generalization of Legendre wavelets. The mechanism is still upon workable implementation of the operational matrix of integration and its derivatives. This method reduces the problems into algebraic equations via the properties of generalized Legendre wavelet (GLW) together with the operational matrix of integration. As a result of this inquiry, the proposed numerical technique based on the GLW has been tested on three linear problems. The proposed numerical technique, based on the GLW, has been examined on three linear problems as a consequence of this investigation. The numerical findings reveal that, in comparison to other existing numerical and analytical methods, this method is quite useful and advantageous for dealing with such situations. The proposed approach is applicable to increasingly complex differential equations.