We propose a tumor growth model that can be parallelized using a classical master/slave design pattern on CUDA/GPU. The probabilistic algorithm on which the model presented here is based has shown excellent performance in obtaining efficient simulations of tumor growth and their implementation in an advanced software development environment. The level of computational resources required to perform the entire probabilistic computation may make the proposed algorithm more complex than similar recent proposals, but its scalability with respect to number of processing nodes currently outperforms other state-of-the-art tumor growth algorithms when it comes to simulating large tumors. As evidence of the higher performance achieved with the CUDA/C++ implementation of the algorithm, we can state that the obtained measurements of processing time outperform those obtained in other recent research work to simulate dense tumor growth.