In HTS transformer with double pancake windings, the perpendicular component of leakage magnetic flux density ($B_{r}$ ) applied to HTS tapes of double pancake windings of HTS transformer acts as a cause to decrease the critical current in HTS tape. So, in this paper, HTS transformer with reciprocal arrangement winding is designed. And in order to investigate the$ B_{r}$ applied to HTS windings, the 2-D non-linear electromagnetic analysis of HTS transformer is performed by using the OPERA 2D. The maximum $B_{r}$ applied to winding of HTS transformer is 0.112 T and the characteristics of HTS transformer were also obtained. But in this type of winding arrangement, reciprocal arrangement, the generated ac-loss to the HTS windings is very high because of the applied $B_{r}$ to HTS windings. Therefore, in order to reduce the generated ac-loss to the HTS windings, the new design of HTS transformer with concentric winding arrangement is presented in this paper and the 2-D non-linear electromagnetic analysis and the ac-loss for HTS transformer with the concentric winding arrangement is also carried out.