Since the advent of deep belief network deep learning technology in 2006, artificial intelligence technology has been utilized in various convergence areas, such as autonomous driving and medical care. Some services requiring fast decision making and action typically work seamlessly with edge computing service model. In autonomous driving of a connected vehicle with vehicle-to-everything (V2X) communication, roadside unit (RSU) acts as an edge computing device and it will make safer service by processing V2X messages fast, sent by vehicles or other devices. IEEE 1609.2 standard provides application message security technology to ensure the security and reliability of vehicle-to-vehicle communication messages. It uses elliptic curve digital signature algorithm (ECDSA) signatures based on the NIST p256 curve for message authenticity. In this paper, we investigate that RSU should be able to verify 3500 ECDSA signatures per second considering the expected maximum number of vehicles on nearby roads (e.g., during rush hour), message transmission rate, and IEEE 802.11p wireless channel capacity. RSU should satisfy this requirement without assistance of hardware-based cryptographic accelerator. For the requirement, we propose a hybrid approach of parallel ECDSA signature verification at high speed by using CPU and GPU, simultaneously. Moreover, we implemented the proposed method in various modern computing environments for RSU and edge computing devices. Through the experiments, we reach the conclusion that GPU can contribute to the required performance of ECDSA signature verification in RSU platform, which could not satisfy the above throughput only with CPU unit. The target platform with Intel Pentium E6500 CPU and GeForce GTX650 GPU can verify 5668 signatures per second with 30% utilization, while CPU in the platform can process only 2640 signatures. Even in a higher-performance edge computing device, we examine experimentally that the performance can be further improved by using the proposed hybrid approach.