Considering the loss of direct visual and tactile information, surgeons require special training programs to obtain sufficient proficiency for laparoscopic surgery. Surgical training simulation systems provide an effective alternative to animal models for repetitive training practices. The purpose of this study was to develop a biomechanical model of large soft organs for simulation of the interactions of a surgical grasper and spleen in real-time. The mechanical behavior of the spleen was molded in detail, including its nonlinear hyper viscoelastic properties, using a mass-spring-damper model. A novel collision detection algorithm was used to determine the tool-tissue contact zones. Force-based and geometry-based boundary conditions were imposed at the contact nodes, respectively, to represent slippage-included and slippage-free grasping conditions. The model’s predictions were validated against the experimental results on a synthetic test sample. Results of simulation of interactions between the grasping tool and the spleen organ indicated that the non-linear rate dependent and stress relaxation behaviors of the tissue was well depicted by the model. Also, the model was capable of reflecting the effect of tool-tissue friction coefficient on the slippage-free or slippage-included grasping behaviors.