A high-moisture extrusion process was used to produce plant-based meat analogues with fibrous structure. Mung bean protein isolate (MBP) and wheat gluten (WG) blend (70:30, w/w) were extruded using a co-rotating twin screw extruder. The optimization of extrusion parameters, including feed moisture content (55–65%, w/w) and barrel temperature (140–160°C), with respect to the textural properties and sensory characteristics of high-moisture meat analogue (HMMA) was investigated using central composite design. An increase in moisture content of the meat analogue led to a decrease in its firmness, hardness, and chewiness determined using instrumental analysis. These results were consistent with hardness, number of chews, and roughness scores evaluated by the trained panelists. Moreover, the microstructure and visual observations showed that fibrous alignment tended to become less compact and form finer strands with an increasing moisture content. However, the barrel temperature had no or slight impact on texture properties of the meat analogue. Acceptance test result revealed that the liking scores of all attributes tended to increase with an increasing extrudate moisture content. The optimized process conditions according to the maximized acceptance score included 65% feed moisture content and extrusion temperature of 140°C with 0.644 desirability. The acceptance scores of the resulting HMMA ranged from 6.4 to 6.7 on a 9-point hedonic scale.