The　identification　of　separable　nonlinear　models,　prevalent　in　tasks　such　as　signal　analysis,　image　processing,　time　series　analysis,　and　machine　learning,　presents　a　non-convex　optimization　challenge　that　necessitates　the　development　of　efficient　identification　algorithms.　The　Variable　Projection　(VP)　algorithm　has　been　proven　to　be　quite　effective　for　addressing　these　problems;　however,　traditional　VP　relying　on　the　Hessian　matrix　and　its　inverse　are　highly　time-consuming　and　unsuitable　for　complex,　large-scale　applications.　This　letter　introduces　a　novel　approach　that　employs　the　exponential　moving　average　of　gradient　and　gradient　estimation　bias　to　indirectly　estimate　the　curvature　of　the　objective　landscape,　proposing　a　Moving　Average-based　Variable　Projection　method　(MAVP).　The　proposed　algorithm　utilizes　only　gradient　information　and　can　properly　tackle　the　coupling　relationships　between　different　parameters　during　the　optimization　process,　thereby　achieving　faster　convergence.　Numerical　results　on　nonlinear　time　series　analysis　and　image　reconstruction　demonstrate　that　the　MAVP　algorithm　exhibits　significant　efficiency　and　effectiveness.