This research proposes a new Markov chain Monte Carlo (MCMC) sampler called Gamma-type Polar Metropolis Hit-and-Run (PMHR-G). The new sampler is developed from the Normal-type Polar Metropolis Hit-and-Run (PMHR-N) for parameter estimation conditional on a complete ranking of the variables. A study is performed to compare the efficiency among PMHR-G, PMHR-N and another two well-known MCMC sampler, namely Gibbs sampler and Hit-and-Run sampler. The upper confidence bound of the corrected potential scale reduction factor (PSRF) is employed as the performance measures, along with the graph of key variables’ cumulative means. The study is done on simulated data sets at three different dimensions (10, 50, 100), four different correlation coefficients (0, 0.5, 0.75, 0.9) and three different mean vectors (zero vector, increasing sequences from -1 to 1, decreasing sequences from 1 to -1). They form in total 36 experimental cases. The results show that the two performance criteria agree on 25 experimental cases (69.44%). In the cases that the two criteria, is measurable, agree on 13 experimental cases, PMHR-G performs best in 12 the cases (92.31%) and Gibbs performs best in 1 the remaining (7.69%).