Purpose Compared with cusp height and area deviation ratio, volume error (VE) caused by the layer height could represent the stair-case effect more comprehensively. The proposed relative volume error (RVE)-based adaptive slicing method takes VE rather than cusp height as slicing criteria, which can improve part surface quality for functionalized additive manufacturing. Design/methodology/approach This paper proposes a volumetric adaptive slicing method of manifold mesh for rapid prototyping based on RVE. The pre-height sequences of manifold mesh are first preset to reduce the SE by dividing the whole layer sequence into several parts. A breadth-first search-based algorithm has been developed to generate a solid voxelization to get VE. A new parameter RVE is proposed to evaluate the VE caused by the sequence of the layer positions. The RVE slicing is conducted by iteratively adjusting the layer height sequences under different constraint conditions. Findings Three manifold models are used to verify the proposed method. Compared with uniform slicing with 0.2 mm layer height, cusp height-based method and area deviation-based method, the standard deviations of RVE of all three models are improved under the proposed method. The surface roughness measured by the confocal laser scanning microscope proves that the proposed RVE method can greatly improve part surface quality by minimizing RVE. Originality/value This paper proposes an RVE-based method to balance the surface quality and print time. RVE could be calculated by voxelized parts with required accuracy at a very fast speed by parallel.