Cloud computing enables computational resource-limited devices to economically outsource much computations to the cloud. Modular exponentiation is one of the most expensive operations in public key cryptographic protocols, and such operation may be a heavy burden for the resource-constraint devices. Previous works for secure outsourcing modular exponentiation which use one or two untrusted cloud server model or have a relatively large computational overhead, or do not support the 100% possibility for the checkability. In this letter, we propose a new efficient and verifiable algorithm for securely outsourcing modular exponentiation in the two untrusted cloud server model. The algorithm improves efficiency by generating random pairs based on EBPV generators, and the algorithm has 100% probability for the checkability while preserving the data privacy.