We propose the Dantzig selector based on the l1-q (1<q≤2) minimization model for the sparse signal recovery. First, we discuss some properties of l1-q minimization model and give some useful inequalities. Then, we give a sufficient condition based on the restricted isometry property for the stable recovery of signals. The l1-2 minimization model of Yin-Lou-He is extended to the l1-q minimization model.