We　propose　and　analyze　an　extended　Fourier　pseudospectral　(eFP)　method　for　the　spatial　discretization　of　the　Gross-Pitaevskii　equation　with　low　regularity　potential　by　treating　the　potential　in　an　extended　window　for　its　discrete　Fourier　transform.　The　proposed　eFP　method　maintains　optimal　convergence　rates　with　respect　to　the　regularity　of　the　exact　solution　even　if　the　potential　is　of　low　regularity　and　enjoys　similar　computational　cost　as　the　standard　Fourier　pseudospectral　method,　and　thus　it　is　both　efficient　and　accurate.　Furthermore,　similar　to　the　Fourier　spectral/pseudospectral　/pseudospectral　methods,　the　eFP　method　can　be　easily　coupled　with　different　popular　temporal　integrators　including　finite　difference　methods,　time　-splitting　methods　and　exponential　-type　integrators.　Numerical　results　are　presented　to　validate　our　optimal　error　estimates　and　to　demonstrate　that　they　are　sharp　as　well　as　to　show　its　efficiency　in　practical　computations.