This paper proposes a Douglas-Rachford splitting algorithm partially based on Bregman distance (referred to as PBDR algorithm hereinafter) for the minimization problem of the sum of non-convex functions. By introducing the Bregman distance function, this algorithm non-Euclidean generalizes some subproblems in the classical Douglas-Rachford splitting framework, thereby extending the application of this type of algorithm in non-Euclidean geometric structures. In terms of theoretical analysis, this paper constructs a value function and combines the Kurdyka-Lojasiewicz property to prove the global convergence of the algorithm’s iterative sequence. In numerical experiments, this paper takes non-convex feasibility problems as the test benchmark and designs special numerical calculations for subproblems involving Bregman distance. The research results show that the PBDR algorithm is significantly superior to traditional algorithms in terms of convergence speed, computational accuracy, and numerical stability.