IEEE　Coded　aperture　snapshot　spectral　imager　(CASSI)　provides　a　potential　solution　to　recover　the　3D　hyperspectral　image　(HSI)　from　a　single　2D　measurement.　The　latest　proposed　design　of　dual-camera　compressive　hyperspectral　imager　(DCCHI)　can　collect　more　information　simultaneously　with　CASSI　to　improve　the　reconstruction　quality.　The　main　bottleneck　now　lies　in　the　high　computation　complexity　of　the　reconstruction　methods,　which　hinders　the　practical　application.　In　this　paper,　we　propose　a　fast　parallel　implementation　based　on　DCCHI　to　reach　a　stable　and　efficient　HSI　reconstruction.　Specifically,　we　develop　a　new　optimization　method　for　the　reconstruction　problem,　which　integrates　the　alternative　direction　multiplier　method　(ADMM)　with　the　total　variation　(TV)　based　regularization　to　boost　the　convergence　rate.　Then,　to　improve　the　time　efficiency,　a　novel　parallel　implementation　based　on　GPU　is　proposed.　The　performance　of　the　proposed　method　is　validated　on　both　synthetic　and　real　data.　The　experiment　results　demonstrate　our　method　has　a　significant　advantage　in　time　efficiency　while　maintaining　a　comparable　reconstruction　fidelity.