The main purpose of this paper is to consider the initial-boundary value problem for the 1D mixed nonlinear Schr(o)dinger equation ut =iαuxx +βu2(ū)x + γ|u|2ux + i|u|2u on the half-line with inhomogeneous boundary condition.We combine Laplace transform method with restricted norm method to prove the local well-posedness and continuous dependence on initial and boundary data in low regularity Sobolev spaces.Moreover,we show that the nonlinear part of the solution on the half-line is smoother than the initial data.