This study aims to extend the original Eulerian space-time conservation element and solution element (CE/SE) method to the Eulerian-Lagrangian framework to solve the gas-particle two-phase detonation problems. The gas-aluminum particle two-phase detonations are numerically investigated by the developed Eulerian-Lagrangian code, in which the gas-phase compressible Euler equations are solved by our in-house CE/SE scheme based on quadrilateral meshes. Additionally, the particle-phase Lagrangian equations, together with the stiff source terms of interphase interactions and chemical reactions, are explicitly integrated via the operator-splitting technique. A dynamic data structure is introduced to store particle information to overcome the tremendous communication costs when applying message passing interface parallel to the Eulerian-Lagrangian framework. The code is shown to be of better parallel efficiency in moderate-scale computations than that uses static arrays. Comparisons with previous one-dimensional and two-dimensional simulation results and experimental observations are conducted to demonstrate the accuracy and reliability of the developed Eulerian-Lagrangian CE/SE code in gas-particle two-phase detonation simulations. Moreover, the code is also applied to simulate polydisperse gas-particle detonations which is close to a realistic scenario, and significant differences in detonation characteristics are found when compared with the monodisperse counterparts. The great demands of using the Eulerian-Lagrangian method to obtain more physics-consistent gas-particle detonation results are addressed, which the traditional Eulerian-Eulerian simulations fail to observe. (C) 2019 Elsevier Inc. All rights reserved.