One of the most common and practical methods in controlling the local scour around bridge pier is to place a protective riprap layer. Due to various uncertainties in the design of this countermeasure method, in the present study, the reliability analysis method was applied for the design of a riprap size around a real bridge pier as a case study. Therefore, four different methods including First Order Second Moment, First Order Reliability Method, Spread Sheet and Monte Carlo Simulation Technique were used to quantify the uncertainties and design of riprap size. The results showed that the probability of riprap size failure, which was calculated by the empirical equation and the  use of the mean value of effective parameters in the case study, was very high,  nearly 34%. In the following, the relationship between safety factor and the reliability index at the site of this case study was determined. Finally, in order to achieve more realistic results, the hydraulic correlation coefficient between depth and flow velocity parameters and its effect on the probability of the riprap failure were studied. It was shown that the correlation coefficient between these two hydraulic parameters was very high and more than 90%, and its maximum effect on the probability of the riprap failure was less than 10%.