This　paper　focuses　on　the　error　analysis　of　a　first-order,　time-discrete　scheme　for　solving　the　nonlinear　Allen-Cahn　equation.　The　discretization　of　the　nonlinear　potential　is　achieved　through　the　EIEQ　method,　which　employs　an　auxiliary　variable　to　linearize　the　nonlinear　double-well　potential　effectively.　The　energy　stability　of　the　scheme　is　demonstrated,　along　with　its　decoupled　type　implementation.　Under　a　set　of　reasonable　assumptions　related　to　boundedness　and　continuity,　an　extensive　error　analysis　is　performed.　This　analysis　results　in　the　establishment　of　L-2　and　H-1　error　bounds　for　the　numerical　solution.　Furthermore,　a　variety　of　numerical　examples　are　conducted　to　illustrate　the　accuracy　of　the　EIEQ　scheme,　highlighting　its　effectiveness　in　addressing　complex　dynamical　systems　governed　by　the　Allen-Cahn　equation.