In this paper, we study the problem of computing quality fault-tolerant virtual backbone in homogeneous wireless network, which is defined as the $k$-connected $m$-dominating set problem in a unit disk graph. This problem is NP-hard, and thus many efforts have been made to find a constant factor approximation algorithm for it, but never succeeded so far with arbitrary $k\geq 3$ and $m\geq 1$ pair. We propose a new strategy for computing a smaller-size 3-connected $m$-dominating set in a unit disk graph with any $m\geq 1$. We show the approximation ratio of our algorithm is constant and its running time is polynomial. We also conduct a simulation to examine the average performance of our algorithm. Our result implies that while there exists a constant factor approximation algorithm for the $k$-connected $m$-dominating set problem with arbitrary $k\leq 3$ and $m\geq 1$ pair, the $k$-connected $m$-dominating set problem is still open with $k>3$ .