Age-specific mortality rate is a key parameter to estimate life expectancy based on age-group population. However, it is impossible to estimate life expectancy in non-sampling years (i.e., without census or 1% population sampling survey) due to the loss of age-specific mortality rate in statistical yearbooks. To estimate time-series life expectancy at China's provincial level in the non-sampling years, this paper firstly proposes a time-series estimation algorithm based on Lagrange interpolation by combining census data with population data from statistical yearbooks. We selected six provinces in central China as study areas and estimated provincial time-series life expectancy in non-sampling years by four algorithms, i.e., linear interpolation and quadratic polynomial interpolation in direct and indirect ways. And the absolute accuracy of estimating time-series life expectancy indicates that the accuracy of linear interpolation for proportions of population by age group (i.e. indirect method) is significantly higher than that of quadratic polynomial interpolation (i.e. indirect method) and time-series interpolation of life expectancy (i.e. direct method) based on two methods, which is proposed as a recommendation algorithm. This study provides a new and feasible way to acquire the provincial time-series life expectancy in non-sampling years, which lays a foundation for the more accurate trend analysis of life expectancy in China.