The aim of this paper is to study a degenerate double-phase parabolic problem with strongly nonlinear source under Dirichlet boundary conditions, proving the existence of a non-negative periodic weak solution. Our proof is based on the Leray-Schauder topological degree, which poses many problems for this type of equations, but has been overcome by using various techniques or well-known theorems. The system considered is a possible model for problems where the studied entity has different growth coefficients, p and q in our case, in different domains.