Using a connected dominating set (CDS) to serve as a virtual backbone of a wireless sensor network is an effective way to save energy and alleviate broadcasting storm. Since nodes may fail due to accidental damage or energy depletion, it is desirable to construct a fault tolerant CDS, which can be modeled as a k-connected m-fold dominating set ((k, m)-CDS for short). A subset of nodes C ⊆ V(G) is a (k, m)-CDS of G if every node in V(G)\C is adjacent with at least m nodes in C and the subgraph of G induced by C is k-connected. In this paper, we present an approximation algorithm for the minimum (3, m)-CDS problem with m > 3, which has size at most γ times that of an optimal solution, where γ = α + 8 + 21n(2α - 6) for α > 4 and γ = 3α + 2 In 2 for α <; 4, and α is the approximation ratio for the minimum (2, m)-CDS problem. This is the first performance-guaranteed algorithm for the minimum (3, m)-CDS problem in a general wireless network, and improves previous performance ratio in a homogeneous wireless sensor network by a large amount.