Recently, the $��_{p}$-norm regularization minimization problem $(P_{p}^��)$ has attracted great attention in compressed sensing. However, the $��_{p}$-norm $\|x\|_{p}^{p}$ in problem $(P_{p}^��)$ is nonconvex and non-Lipschitz for all $p\in(0,1)$, and there are not many optimization theories and methods are proposed to solve this problem. In fact, it is NP-hard for all $p\in(0,1)$ and $��>0$. In this paper, we study two modified $��_{p}$ regularization minimization problems to approximate the NP-hard problem $(P_{p}^��)$. Inspired by the good performance of Half algorithm and $2/3$ algorithm in some sparse signal recovery problems, two iterative thresholding algorithms are proposed to solve the problems $(P_{p,1/2,��}^��)$ and $(P_{p,2/3,��}^��)$ respectively. Numerical results show that our algorithms perform effectively in finding the sparse signal in some sparse signal recovery problems for some proper $p\in(0,1)$.