In this paper an improved architecture of Extended-Euclidean Algorithm (EEA) for finding Modular Multiplicative Inverse (MMI) and Jacobi symbol is proposed. Implementation is done using Hardware Description Language HDL (Verilog program) and synthesized with XILINX ISE DESIGN SUITE14.2 with device vertex 6 xc6vlx760-2-ff1760, and Experimental results are compared with the existing Extended-Euclidean Algorithm (EEA). From the synthesized results offered the requirement of slice LUTs and Slice registers utilization have been reduced by ~17% from its counterpart. The proposed architecture have been used in its practical application to find the modular multiplicative inverse [MMI] and Jacobi symbol.