Belief propagation (BP) algorithm is a widely used message-passing method for inference in graphical models. BP on loop-free graphs converges in linear time. But for graphs with loops, BP's performance is uncertain, and the understanding of its solution is limited. To gain a better understanding of BP in general graphs, we derive an interpretable belief propagation algorithm that is motivated by minimization of a localized $α$-divergence. We term this algorithm as $α$ belief propagation ($α$-BP). It turns out that $α$-BP generalizes standard BP. In addition, this work studies the convergence properties of $α$-BP. We prove and offer the convergence conditions for $α$-BP. Experimental simulations on random graphs validate our theoretical results. The application of $α$-BP to practical problems is also demonstrated.