Sequential data may contain a lot of sensitive information， so that directly mining frequent patterns of sequential data would carry significant risk to privacy of individuals. By resisting attackers with any background knowledge， Local Differential Privacy （LDP） can provide more comprehensive protection for sensitive information. Due to the inherent sequentiality and high-dimensionality， it is challenging to mine frequent sequential patterns with the application of LDP. To tackle this problem， a top-k frequent sequential pattern mining algorithm satisfying ε-LDP， called PrivSPM， was proposed. In this algorithm， filling and sampling technologies， adaptive frequency estimation algorithm and frequent item prediction technology were integrated to construct candidate item. Based on the new domain， an exponential mechanism based strategy was employed to perturb the user data， and the final frequent sequential patterns were identified by combining the frequency estimation algorithm. Theoretical analysis proves that the proposed algorithm satisfies ε-LDP. Experimental results on three real datasets demonstrate that PrivSPM algorithm performs better than the comparison algorithm on True Positive Rate （TPR） and Normalized Cumulative Rank （NCR）， and can improve the accuracy of mined results effectively.