In order to improve the reconstruction quality of greedy backtracking algorithm, a forward predictive greedy backtracking algorithm is proposed based on improving the atomic selection mode of support set. Firstly, the Dice coefficient criterion is used to measure the correlation. Then, the forward prediction method is used to select the optimal atomic number introduced by each iteration. Finally, the redundant atoms are deduced to determine the optimal support set and complete the signal reconstruction. Experiments result show that the algorithm preserves the advantages of high efficiency of greedy backtracking algorithm, high robust, and realizes the optimal selection of support set atom. The algorithm can improve the reconstruction precision and success rate.