I will talk about the ratio of the L1 and L2 norms, denoted as L1/L2, to promote sparsity. Due to the non-convexity and non-linearity, there has been little attention to this scale-invariant model. Compared to popular models in the literature such as the Lp model for 0< p< 1 and the transformed L1 (TL1), this ratio model is parameter-free. Theoretically, we present a strong null space property (sNSP) and prove that any sparse vector is a local minimizer of the L1/L2 model provided with this sNSP condition. The experimental results demonstrate the proposed approaches are comparable to the state-of-the-art methods in sparse recovery and work particularly well when the ground-truth signal has a high dynamic range. In addition, a variant of the L1/L2 model to apply to the gradient is also discussed with a proof-of-concept example of the MRI reconstruction.