In this letter, we present a volumetric mapping system that effectively calculates Occupancy Grid Maps (OGMs) and Euclidean Distance Transforms (EDTs) with parallel computing. Unlike these mappers for high-precision structural reconstruction, our system incrementally constructs global EDT and outputs high-frequency local distance information for online robot motion planning. The proposed system receives multiple types of sensor inputs and constructs OGM without down-sampling. Using GPU programming techniques, the system quickly computes EDT in parallel within local volume. The new observation is continuously integrated into the global EDT using the parallel wavefront algorithm while preserving the historical observations. Experiments with datasets have shown that our proposed approach outperforms existing state-of-the-art robot mapping systems and is particularly suitable for mapping unexplored areas. In its actual implementations on aerial and ground vehicles, the proposed system achieves real-time performance with limited onboard computational resources.