In this paper, we present a simple method based on \(C^1\) quadratic polynomial splines that provides the numerical solution of Love’s integral equation. This technique consists in approximating the univariate right section of the kernel of the considered equation by a quadratic quasi-interpolant (QI). The approximate solution is obtained by solving a linear system where the matrix coefficients are computed explicitly. We study the convergence analysis and we show that the method is of order four. Finally, we give some numerical examples that illustrate the theoretical results and the validity of the presented method.