<p>This paper presents a novel class of high-order mass-, energy- and momentum-preserving exponential integrators for solving the derivative nonlinear Schrödinger equation. Firstly, we reformulate the original system into an exponential supplementary variable system based on the idea of the exponential supplementary variable approach, and then the reformulated system is discretized by using the standard Fourier pseudo-spectral method in space and the high-order prediction-correction Lawson Runge–Kutta method in time, respectively. The proposed method is highly efficient, temporally high-order accurate, and simultaneously preserves the mass, energy and momentum in the discrete setting. Finally, numerical experiments validate the accuracy and energy-preserving properties.</p>