The explosive growth of mobile users has been increasing in the past few years. In this paper, an efficient authentication scheme for distributed mobile cloud computing is proposed. This proposed scheme enables the users to access multiple service providers with a single private key. Instead of opting traditional public key cryptosystem like RSA, the proposed scheme uses bilinear pairing technique for effective anonymous authentication. This scheme supports mutual authentication. In our proposed scheme, mobile cloud users and service providers are only allowed to communicate during the authentication process. The third party is considered to be trusted and it participates in the registration of mobile cloud users and the service providers. In addition, our proposed scheme prevents the malicious mobile users and service providers through the third party revocation mechanism. With this design, our proposed scheme reduces the computation cost during the anonymous mutual authentication between the mobile cloud user and the service provider. Performance analysis is conducted to show that our proposed scheme is computationally efficient in comparison with the previously used schemes in the literature.