Wireless sensor networks include a set of sensors being network nodes and a base station. The objective of such systems is to monitor changes which might occur at targets' location. Consequently, assuring the network connectivity is compulsory to maintain a continuous monitoring of given set of targets. However, sensor nodes sometimes stop functioning due to being physically damaged or running out of energy (battery), thus affecting to the connectivity of the system. This paper considers the target coverage with connectivity fault-tolerance problem in wireless sensor networks. The goal of this problem is to come up with a network topology consisting of the least number of sensor nodes that not only offers the greatest target coverage but also maintains the network connectivity even when one random node is defected. This is an NP-Complete combinatorial optimization problem. One heuristic algorithm is proposed to solve the target coverage with connectivity fault-tolerance problem and it is tested on 15 randomly generated instances. Experimental results illustrate a good performance achieved in terms of target coverage, connectivity and fault-tolerance.