The interaction simulations between particles and structures are often performed in the context of the combined discrete-finite element (DEM-FEM) method, where an efficient, robust and accurate contact algorithm for challenging contact problems is essential. A three-dimensional (3D) discrete and finite element contact algorithm, named ZGL here, has been proposed in our research group (Zang, M.Y. et al., 2011. A contact algorithm for 3D discrete and finite element contact problems based on penalty function method. Comput. Mech. 48, 541-550.). Despite being quite well-established, ZGL algorithm may lack efficiency, robustness and accuracy in certain situations, e.g., when special mesh pattern is applied. However, since such cases are readily to appear in practice engineering application, an algorithm named DZCeII is developed to resolve these issues and thus significantly applicable to challenging contact problems. The proposed DZCell algorithm includes an improved global phase to directly find the potential segments rather than the nearest node for discrete elements as contact counterparts. Furthermore, both the memory cost and time consumption of this algorithm are linear, and the algorithm is readily to extend to parallel computing. Several numerical examples demonstrate the achievable improvements in terms of efficiency, robustness and accuracy for 3D contact analysis and validate the capability of the DZCeII algorithm in the granular science and mechanical engineering. (C) 2016 Elsevier B.V. All rights reserved.