In this paper, we propose a quantum circuit for Curve25519, the elliptic curve used in Elliptic-Curve Cryptography (ECC). First, we implemented the addition, subtraction, and multiplication (squaring) operations on prime fields as quantum circuits. These circuits are flexible, allowing for modifications to the prime value and input length, making them applicable not only to Curve25519 but also to other cryptographic systems. We optimally adjusted the algorithmic sequences of the Point Doubling and Point Addition functions used in Curve25519 for quantum circuit implementation. Additionally, we strategically placed inverse operations to eliminate or reduce the use of temporary qubits in the algorithm. As a result of our qubit optimization, we reduced the total number of qubits in the Curve25519 circuit by 2,483.