This study presents a mathematical modelling to investigate the wave propagation behaviour in laminated natural fibre-reinforced composite plates integrated with surface bonded piezoelectric materials. To model wave dynamics, the constitutive relations, and governing equations of wave motion are derived based on different plate theories and Maxwell's electricity equation due to the surface bonded piezoelectric materials with the closed-circuit electrical boundary condition and transverse poling direction. The influence of natural fibres, as the reinforcing material of the host laminated composite plate, on wave propagation is studied and compared with the effects of synthetic fibres (i.e., carbon, Kevlar, and E-glass). The effects of other factors such as fibre volume fraction, laminate stacking sequence, and the presence of piezoelectric materials on wave dynamics are also investigated. The results of the wave propagation analysis reveal that the impact of different parameters on wave dynamics depends on the range of wavenumbers and wave mode numbers considered. It is found that some parameters may exhibit a noticeable influence on wave velocities, while others may have a negligible effect. The effect of piezoelectric materials on wave velocities in composite plates reinforced with natural fibres e.g., bamboo fibres, may differ from that observed in synthetic fibre-reinforced composite plates.