There are big limitations in 3D-printed parts for engineering applications due to their weak transverse mechanical properties when using fused filament fabrication (FFF). Accordingly, this study introduces a novel layer misalignment printing (LMP) method inspired by the meso-structural pattern in FFF. First, the effect of printing temperature on mesoscopic structural characteristics in LMP and the conventional approach of layer aligned printing (LAP) were compared and analysed. Second, in view of the periodic distribution characteristics, specific multi-scale numerical models based on the in-plane cohesive method and linear softening constitutive relation were developed to explore the effect of meso-pores on the mechanical properties. The proposed numerical models were applied to predict macroscopic mechanical responses and analyse mesoscopic damage mechanisms. Then, standard test specimens, oriented perpendicular and parallel to the printing direction, were fabricated using both printing methods for quasi-static tensile testing and characterisation. Through microscopic characterisation and statistical analysis, it is found that when using LMP, porosities are decreased by 0.4 %, 5.4 %, and 8.1 % in comparison to those when using LAP, at printing temperatures of 275 °C, 250 °C and 225 °C, respectively. Experimental results show that the average longitudinal and transversal elastic moduli of LMP-based specimens are increased by 7.8 % and 23.5 %, respectively, when compared to LAP-based ones. Meanwhile, the longitudinal and transversal tensile strengths achieve increments by 6.3 % and 26.1 %, respectively. Last, numerical results agree well with experimental results, proving the effectiveness of the proposed multi-scale methods. More importantly, the LMP method is well proven as an effective and promising method to improve the mechanical properties of printed parts via FFF.