A triangular element based on the Mindlin's plate theory has been developed for the analysis of composite plates. The element has six nodes (at the vertices and mid-sides of the triangle) each containing five degrees of freedom--- in- plane displacements $u$, $v$, transverse displacement $w$, and cross-sectional rotations $\theta_x$ ($=\frac{\partial w}{\partial x}+\gamma_x$) and $\theta_y$ ($=\frac{\partial w}{\partial y}+\gamma_y$). The key concept of assuming independent shear rotations $\gamma_x$ and $\gamma_y$ enables a high order of displacement to be modelled with relatively fewer degrees of freedom. Representing the field variables $u$, $v$, $w$, $\gamma_x$ and $\gamma_y$ with complete polynomials of suitable order maintain the proper hierarchy of deflection, rotation, moment and shear, and averts shear locking. $C_1$ compatibility required in the element is kept unsatisfied. On the other hand patch test is passed and the element is free from spurious modes. Numerical examples on deflection of composite plates prove the efficacy of the proposed element.