This paper considers estimating unknown parameters of a new Pareto-type distribution based on Type-I hybrid censoring. First, maximum likelihood and Bayesian method, under squared error and LINEX loss functions, are applied for estimating the parameters involved. The highest posterior density intervals are discussed as well. We establish optimum censoring schemes with respect to cost function optimality criteria. Monte Carlo simulations are implemented to compare different methods and finally, a real data set representing the duration of remission of leukemia patients who were treated by a specific drug is analyzed for illustrative purposes.