In the present work, the effect of the gate-to-drain capacitance ($C_{gd}$) on the noise performance of a symmetric tied-gate $In_{0.52}Al_{0.48}As/In_{0.53}Ga_{0.47}As$ double-gate HEMT is studied using an accurate charge control based approach. An analytical expression for the gate-to-drain capacitance is obtained. In terms of the intrinsic noise sources and the admittance parameters ($Y_{11}$ and $Y_{21}$ which are obtained incorporating the effect of $C_{gd}$), the various noise performance parameters including the Minimum noise figure and the Minimum Noise Temperature are evaluated. The inclusion of gate-to-drain capacitance is observed to cause significant reduction in the Minimum Noise figure and Minimum Noise Temperature especially at low values of drain voltage, thereby, predicting better noise performance for the device.