Many works are designed to improve efficiency or enhance security and privacy of publicly-auditable cloud storage. However, building timeliness for cloud storage has not been well studied. Few works presented time-sensitive cloud storage and only focused on specific issues, such as the earliest creation time of files or resistance against a procrastinating auditor. Therefore, there leaves an absence of building traceable timeliness for publicly-auditable cloud storage. In this paper, we propose a solution PPTPS to build Privacy-Preserving auditable service with Traceable timeliness for Public cloud Storage. First, we use the security properties of the blockchain to provide a time-stamp for each phase. It enables the timeliness of cloud storage. Second, we construct efficient publicly-verifiable cloud storage. Third, a customized random mask solution is proposed to prevent privacy leakage during the auditing phase. Moreover, we formally proved the security of PPTPS. At last, experimental results demonstrate that PPTPS is economically sound and technically viable.