Early prediction of sepsis onset can notify clinicians to provide timely interventions to patients to improve their clinical outcomes. The key question motivating this work is: given a retrospective patient cohort consisting of multivariate clinical time series (e.g., vital signs and lab measurement) and patients' demographics, how to build a model to predict the onset of sepsis six hours earlier? To tackle this challenge, we first used a recurrent imputation for time series (RITS) approach to impute missing values in multivariate clinical time series. Second, we applied temporal convolutional networks (TCN) to the RITS-imputed data. Compared to other sequence prediction models, TCN can effectively control the size of sequence history. Third, when defining the loss function, we assigned custom timedependent weights to different types of errors. We achieved 9th place (team name = prna, utility score = 0.328) at the 2019 PhysioNet Computing in Cardiology Challenge, which evaluated our proposed model on a real-world sepsis patient cohort. At a follow-up 'hackathon' event, held by the challenge organizers, an improved version of our algorithm achieved 2nd place (utility score = 0.342).