The 3D Concrete Printing technology (3DCP) has developed fast in the past few years. Compared to conventional construction method, the 3DCP technology offers an advantage in speed and cost. However, the surface of a structure from 3DCP technology requires post-finishing processes as the direct outcome suffers from low quality surface finish problem, such as jagged surface and staircase effect. This study aims to improve the surface finish quality in 3DCP using a developed novel variable-geometry nozzle that can directly control the extrudate geometry during the printing process at every layer. The nozzle assembly features an adjustable nozzle outlet geometry that can be controlled along the process. The mechanism requires a slicing algorithm to determine the extrudate geometry at every layer based on the designated printed structure. The corresponding algorithm was also developed and will be presented in this paper. Subsequently, the functionality of the proposed method was validated with a case study of manufacturing a structure with curved outer-surface geometry (an arch).