In this paper, an inventory model with general ramp-type demand rate, partial backlogging of unsatisfied demand and time-varying holding cost is considered; where the “Time-varying holding cost” means that the holding cost is a function of time, i.e. it is time dependent. The model is studied under the following different replenishment policies: (1) starting with no shortages (2) starting with shortages. Two component demand rate has been used. The backlogging rate is any non-increasing function of the waiting time up to the next replenishment. The optimal replenishment policy is derived for both the above mentioned policies.