Clinicians and oncologists believe that tumor growth has unpredictable dynamics. For this reason they encounter many difficulties in the treatment of cancer. Mathematical modeling is a great tool to improve our better understanding of the complicated biological system of tumor growth. Also, it can help to identify states of the disease and as a result help to predict later behaviors of the tumor. Having an insight into the future behaviors of the tumor can be very useful for the oncologists and clinicians to decide on the treatment method and dosage of the administered drug. This paper suggests that a suitable model for the tumor growth system should be a discrete model capable of exhibiting periodic and complex chaotic dynamics. This is the key feature of the proposed model. The model is validated here through experimental data and its potential dynamics are analyzed. The model can explain many biologically observed tumor states and dynamics, such as exponential growth, and periodic and chaotic behaviors in the steady states. The model shows that even an avascular tumor could become invasive under certain conditions.