An intuitionistic fuzzy random variable (IFRV) handles ambiguous, incomplete and ill-known data or information along with statistical variability, and deals with fuzzy number, grade of membership and nonmembership functions and probability distribution function. So, taking such advantages of IFRV, we extend the classical continuous review inventory system in intuitionistic fuzzy random (IFR) environment by considering demand rate as IFRV. Due to uncertain variability, demand may suddenly increase, consequently, item shortage(stock out) may occur in the inventory system. To minimize the shortage quantity, fuzzy service level constraint and reorder level pertaining to safety stock are considered here. Service level constraint ensures that a certainfraction of demand to be fulfilled by on-hand inventory, whereas safety stock is kept against anticipation of shortage. Furthermore, we develop a methodology to compute the fuzzy expected shortage quantity for IFR inventory system, and determine the order quantity and reorder level. The proposed model is illustrated with numerical example and sensitivity analysis by changing the values of key parameters, which also helps in delineating the managerial insights.