We　propose　a　time-splitting　sine-pseudospectral　(TSSP)　method　for　the　biharmonic　nonlinear　Schr　&　ouml;dinger　equation　(BNLS)　and　establish　its　optimal　error　bounds.　In　the　proposed　TSSP　method,　we　adopt　the　sine-pseudospectral　method　for　spatial　discretization　and　the　second-order　Strang　splitting　for　temporal　discretization.　The　proposed　TSSP　method　is　explicit　and　structure-preserving,　such　as　time　symmetric,　mass　conservation　and　maintaining　the　dispersion　relation　of　the　original　BNLS　in　the　discretized　level.　Under　the　assumption　that　the　solution　of　the　one　dimensional　BNLS　belongs　to　H-m　with　m　＞=　9,　we　prove　error　bounds　at　O(tau(2　)+　h(m))　and　O(tau(2　)+　h(m-1))　in　L-2　norm　and　H-1　norm　respectively,　for　the　proposed　TSSP　method,　with　tau　time　step　and　h　mesh　size.　For　general　dimensional　cases　with　d　=　1,2,3,　the　error　bounds　are　at　O(tau(2　)+　h(m))　and　O(tau(2　)+　h(m-2))　in　L-2　and　H-2　norm　under　the　assumption　that　the　exact　solution　is　in　H-m　with　m　＞=　10.　The　proof　is　based　on　the　bound　of　the　Lie-commutator　for　the　local　truncation　error,　discrete　Gronwall　inequality,　energy　method　and　the　H-1-　or　H-2-bound　of　the　numerical　solution　which　implies　the　L-infinity-bound　of　the　numerical　solution.　Finally,　extensive　numerical　results　are　reported　to　confirm　our　optimal　error　bounds　and　to　demonstrate　rich　phenomena　of　the　solutions　including　rapidly　dispersion　in　space　of　high　frequency　waves　and　soliton　collisions.