This　paper　considers　the　stability　and　convergence　results　for　the　Euler　implicit/explicit　scheme　applied　to　the　spatially　discretized　two-dimensional　(2D)　time-dependent　Navier-Stokes　equations.　A　Galerkin　finite　element　spatial　discretization　is　assumed,　and　the　temporal　treatment　is　implicit/explict　scheme,　which　is　implicit　for　the　linear　terms　and　explicit　for　the　nonlinear　term.　Here　the　stability　condition　depends　on　the　smoothness　of　the　initial　data　u(0)　is　an　element　of　H(alpha),　i.e.,　the　time　step　condition　is　tau　＜=　C(0)　in　the　case　of　alpha　=　2,　tau|log　h|　＜=　C(0)　in　the　case　of　alpha　=　1　and　tau　h(-2)　=　C(0)　in　the　case　of　alpha　=　0　for　mesh　size　h　and　some　positive　constant　C(0).　We　provide　the　H(2)-stability　of　the　scheme　under　the　stability　condition　with　alpha　=　0,　1,　2　and　obtain　the　optimal　H(1)　-　L(2)　error　estimate　of　the　numerical　velocity　and　the　optimal　L(2)　error　estimate　of　the　numerical　pressure　under　the　stability　condition　with　alpha　=　1,　2.