The P-384 is one of the standardized elliptic curves by ANSI and NIST. This curve provides a 192-bit security level and is used in the computation of digital signatures and key-agreement protocols. Although several publicly-available cryptographic libraries support the P-384 curve, they have a poor performance. In this work, we present software techniques for accelerating cryptographic operations using the P-384 curve; first, we use the latest vector instructions of Intel processors to implement the prime field arithmetic; second, we devise a parallel scheduling of the complete formulas for point addition law. As a result, on Skylake micro-architecture, our software implementation is 15% and 40% faster than the OpenSSL library for computing ECDSA signatures and the ECDH protocol, respectively.