In this paper, a stochastic framework for uncertainty quantification and global sensitivity analysis of a composite wind turbine blade is presented. Nowadays, wind turbines blades are made up of composite materials and it represents a complex structure with varying material, chord, and twist distribution along the span of the blade. In fact, manufacturing the wind turbine blades to its exact specifications is a challenging task since various sources of uncertainties are introduced unwantedly during design, manufacturing, transportation, and operation. These uncertainties can have adverse effects on the performance and reliability of wind turbine blades and must be accounted for during the design phase. However, performing uncertainty quantification while considering a large number of random parameters as in wind turbine blades is still a computationally-intensive process since it demands a large number of finite element analysis (FEA) calls. Therefore, a computationally efficient and high accuracy approach called polynomial chaos expansion (PCE) with l1-minimization has been implemented which also allows for global sensitivity analysis to estimate the influence of random parameters on the stochastic responses. The presented approach was tested by considering the randomness in material, geometric, and loading conditions, and the influence of randomness on natural frequencies and failure of an NREL 5MW wind turbine blade was assessed. The results demonstrated that it can provide high-accuracy information regarding the variation of the responses as well as the influential random parameters at an affordable computational cost. Therefore, this study will be influential in understanding the structural behavior and improving the reliability of composite wind turbine blades.