Tensor completion is important to many areas such as computer vision, data analysis, and signal processing. Previously, a category of methods known as low-rank tensor completion has been proposed and developed, involving the enforcement of low-rank structures on completed tensors. While such methods have been constantly improved, none considered exploiting the numerical properties of tensor elements. This work attempts to construct a new methodological framework called GCDTC (Generalized CP Decomposition Tensor Completion) based on numerical properties to achieve higher accuracy in tensor completion. In this newly introduced framework, a generalized form of the CP Decomposition is applied to low-rank tensor completion. This paper also proposes an algorithm known as SPTC (Smooth Poisson Tensor Completion) for nonnegative integer tensor completion as an application of the GCDTC framework. Through experimentation with real-life data, it is verified that this method could produce results superior in completion accuracy to current state-of-the-art methodologies.