Virtual Trusted Platform Modules (vTPMs) have been widely used in commercial cloud platforms (e.g. Google Cloud, VMware Cloud, and Microsoft Azure) to provide virtual root-of-trust for virtual machines. Unfortunately, current state-of-the-art vTPM implementations are suffering from confidential data leakage and high performance overhead. In this paper, we present SvTPM, a secure and efficient software-based vTPM implementation based on hardware-rooted Trusted Execution Environment (TEE), providing a whole life cycle protection of vTPMs in the cloud. SvTPM offers strong isolation protection, so that cloud tenants or even cloud administrators cannot get vTPM's private keys or any other sensitive data. In SvTPM, we identify and solve a couple of critical security challenges for vTPM protection with SGX, such as NVRAM replacement attack, rollback attacks, trust establishment, and a fine-grained trusted clock. We implement a prototype of SvTPM on both QEMU and KVM. Performance evaluation results show that SvTPM achieves orders of magnitude of performance gains comparing to the vTPMs protected with physical TPM. The launch time of SvTPM is 2600$\times$ faster than vTPMs built upon hardware TPM. In the micro-benchmarks evaluation, we find that the command execution latency of SvTPM is smaller than or equal to the existing schemes.