Equalization is an important task at the receiver side of a digital wireless communication system, which is traditionally conducted with model-based estimation methods. Among the numerous options for model-based equalization, iterative soft interference cancellation (SIC) is a well-performing approach since error propagation caused by hard decision data symbol estimation during the iterative estimation procedure is avoided. However, the model-based method suffers from high computational complexity and performance degradation due to required approximations. In this work, we propose a novel neural network (NN)-based equalization approach, which is designed by deep unfolding of a model-based iterative SIC method, eliminating the main disadvantages of its model-based counterpart. We compare the achieved bit error ratio performance of the proposed NN-based equalizers with state-of-the-art model-based and NN-based approaches, highlighting the superiority of our approach over all other methods.