The reflection of longitudinal micro-rotational wave at the viscoelastically supported boundary of micropolar half-space is studied in this paper. The viscoelastic boundary is described by spring-dashpot model with parallel or serial connection. Both the spring and the dashpot contribute to the displacements and micro-rotation and the boundary conditions include the force stress and couple stress components. From the boundary conditions, the amplitude ratios and phase shifts of reflection waves with respect to the incident wave are obtained. Further, the energy flux ratios of the reflection waves to the incident wave are estimated. In order to validate the numerical results, the energy flux conservation with consideration of the energy dissipation of dashpot is used. Based on the numerical results, the influences of elastic parameters and viscous parameters are studied, respectively. It is found that the elastic parameters and the viscous parameters have evident influences on the amplitude ratio, the phase shift and the energy partition. The causes resulting in these deviations are related with the instantaneous elasticity of spring and the time-delay effects of dashpot.