The rise of multi-cloud systems has been spurred. For safety-critical missions, it is important to guarantee their security and reliability. To address trust constraints in a heterogeneous multi-cloud environment, this work proposes a novel scheduling method called matching and multi-round allocation (MMA) to optimize the makespan and total cost for all submitted tasks subject to security and reliability constraints. The method is divided into two phases for task scheduling. The first phase is to find the best matching candidate resources for the tasks to meet their preferential demands including performance, security, and reliability in a multi-cloud environment; the second one iteratively performs multiple rounds of re-allocating to optimize tasks execution time and cost by minimizing the variance of the estimated completion time. The proposed algorithm, the modified cuckoo search (MCS), hybrid chaotic particle search (HCPS), modified artificial bee colony (MABC), max-min, and min-min algorithms are implemented in CloudSim to create simulations. The simulations and experimental results show that our proposed method achieves shorter makespan, lower cost, higher resource utilization, and better trade-off between time and economic cost. It is more stable and efficient.