Mobile Ad-hoc Networks (MANET) usage across the globe is increasing by the day. Evaluating a node's trust value has significant advantages since such network applications only run efficiently by involving trustable nodes. The trust values are estimated based on the reputation values of each node in the network by using different mechanisms. However, these mechanisms have various challenging issues which degrade the network performance. Hence, a novel Quality of Service (QoS) Trust Estimation with Black/Gray hole Attack Detection approach is proposed in this research work. Initially, the QoS-based trust estimation is proposed by using a Fuzzy logic scheme. The trust value of each node is estimated by using each node's reputation values which are determined based on the fuzzy membership function values and utilizing QoS parameters such as residual energy, bandwidth, node mobility, and reliability. This mechanism prevents only the black hole attack in the network during transmission. But, the gray hole attacks are not identified which in turn increases the packet drop rate significantly. Hence, the gray hole attack is also detected based on the Kullback-Leibler (KL) divergence method used for estimating the statistical measures. Additional QoS metrics are considered to prevent the gray hole attack, such as packet loss, packet delivery ratio, and delay for each node. Thus, the proposed mechanism prevents both black hole and gray hole attacks simultaneously. Finally, the simulation results show that the effectiveness of the proposed mechanism compared with the other trust-aware routing protocols in MANET.