We propose a well-posed Maxwell-type boundary condition for the linear moment system in half-space. As a reduction model of the Boltzmann equation, the moment equations are available to model Knudsen layers near a solid wall, where proper boundary conditions play a key role. In this paper, we will collect the moment system into the form of a general boundary value problem in half-space. Utilizing an orthogonal decomposition, we separate the part with a damping term from the system and then impose a new class of Maxwell-type boundary conditions on it. Due to the block structure of boundary conditions, we show that the half-space boundary value problem admits a unique solution with explicit expressions. Instantly, the well-posedness of the linear moment system is achieved. We apply the procedure to classical flow problems with the Shakhov collision term, such as the velocity slip and temperature jump problems. The model can capture Knudsen layers with very high accuracy using only a few moments.