Predicting remaining useful life (RUL) is crucial for system maintenance. Condition monitoring makes not only degradation data available for RUL estimation but also categorized health status data for health state identification. However, RUL prediction has been treated as an independent process in most cases even though potential relevance exists with health status detection process. In this paper, we propose a convolution neural network based multi-task learning method to reflect the relatedness of RUL estimation with health status detection process. The proposed method applied to the C-MAPSS dataset for aero-engine unit prognostics supported superior performances to existing baseline models.