<p>In this paper, we present a stabilized high-order exponential integrator for solving the regularized logarithmic Schrödinger equation, which simultaneously satisfies discrete analogues of the mass and energy conservation laws. The key ingredient of our method is first to reformulate the original system into a stabilized exponential supplementary variable system by combining the exponential supplementary variable method with the stabilized method, and then the reformulated system is discretized by using the sine pseudo-spectral approximation for spatial discretization and the high-order prediction-correction Lawson Runge-Kutta method for temporal discretization, respectively. The proposed method is computationally efficient, temporally high-order accurate, and conserves both mass and energy in the discrete setting. Finally, numerical results demonstrate the remarkable accuracy and numerical stability of our newly developed methods in comparison with the existing high-order structure-preserving methods in the literature.</p>