Three novel types of multi-cell tubular structures with pre-folded origami patterns were proposed in this paper, aimed at reducing the initial peak force and the crushing force fluctuation while maintaining or increasing the specific energy absorption during uniaxial crush. Experimentally validated finite element modelling was conducted to study the influence of geometric parameters on the mechanical properties. Optimal designs were obtained through multi-objective optimization. The results showed that predesigned origami patterns governed the buckling process of the tubes and quintuple-cell origami tubes could absorb the highest energy in crush with significantly reduced initial peak force and the crushing force fluctuation.