In this paper, the high-$T_c$ , superconductor (HTS) microstrip patch antenna which is directly coupled to a microstrip transmission line is designed and the numerical solution which evaluate near electromagnetic field of HTS antenna is presented. This solution uses the interpolation function with the vector edge triangular element. The advantage of this element is the elimination of spurious solutions attributed to the lack of enforcement of the divergence condition. The results of this method have a good agreement with $TM_10$ mode in HTS microstrip patch antenna and show that the computation of resonant length considering the fringing capacitance effect at radiating edge are proper.