Abstract: The stochastic online scheduling problem is considered on a single machine with simple linear deteriorating jobs. All jobs arrive online over time, the scheduler has no any information about the jobs that would arrive in the future. Only when the jobs arrive, the scheduler can know the expectation of job's processing time immediately, and the expectation of processing time was a simple linear function that depends on the starting time of processing the job. Until the jobs are completed, their actual processing time could be known. The goal function of this problem is to minimize the expectation of total completion time of all jobs. An SHIFT-SDR algorithm is presented to this stochastic online problem by shifting the release time of jobs, with the competitive ratio 1+b_max. This ratio matches the lower bound of deterministic case that is studied by LIU M et al. Thus, this can show that our algorithm is the best possible online algorithm for the problem that we studied.