In this paper, we present an approach for performance enhancement of an antenna for millimeter wave (mmWave) applications. From mmWave band, a 30 GHz frequency is selected for designing a patch antenna as it is suitable for the number of applications. Then the designed antenna is modified by inserting a capacitive structure i.e., inter-digital capacitor (IDC) for better impedance matching. Insertion of IDC structure results in antenna size reduction along with the increased directivity and enhancement in gain. Similarly, this technique is capable of providing extra resonance with an advantage of fine tuning, as it offers control over both resonating frequencies independently. Further, a linear antenna array is designed with the same approach for mutual coupling analysis. From the results, it has been found that this technique is also capable of providing mutual coupling mitigation. Thus insertion of IDC structure provides overall performance enhancement in mmWave antenna.