This paper studies a single machine scheduling problem with time-dependent learning and setup times. Time-dependent learning means that the actual processing time of a job is a function of the sum of the normal processing times of the jobs already scheduled. The setup time of a job is proportional to the length of the already processed jobs, that is, past-sequence-dependent (psd) setup time. We show that the addressed problem remains polynomially solvable for the objectives, i.e., minimization of the total completion time and minimization of the total weighted completion time. We also show that the smallest processing time (SPT) rule provides the optimum sequence for the addressed problem.