The nonlinear unified strength criterion proposed by authors in 2010 is adopted as the yield function and the plastic potential function for concrete. Four original material parameters of the nonlinear unified strength criterion are derived as functions of four conventional strength indexes of concrete. A three-dimensional elastoplastic constitutive model for concrete is then developed by using hardening and softening functions that are determined from the uniaxial compressive stress–strain relationship. The performance of the constitutive model is evaluated by comparing prediction and experimental data from literatures. The comparison shows the model is able to reasonably describe the three-dimensional strength characteristics, strain softening behavior after the peak stress and the dilatancy of various concretes. Moreover, the proposed model is integrated in the general finite element package ABAQUS via UMAT to simulate the deformation process of reinforced concrete columns under eccentric compression. The simulations show that the proposed constitutive model is able to describe the nonlinear mechanical behavior under complex stress states with high computational efficiency.