The acoustic and structural dynamic properties of vehicles—often referred to as Noise, Vibration, Harshness (NVH)—form a crucial criterion during product development. To reduce iterations with physical prototypes, NVH simulation models are well established. In early development phases, many parameters of NVH models, such as material and contact properties, are either assumed based on empirical values or have to be measured. In both cases, the value of these parameters is uncertain. Thus, the output of NVH system simulation models such as structure borne or air borne sound is also uncertain and must be quantified. However, applying state-of-the-art uncertainty analysis methods to NVH simulation models considering all uncertain input parameters is inefficient due to their high computation time. Therefore, this paper presents a method of coupled sensitivity (SA) and uncertainty analysis (UA), which enables the efficient uncertainty calculation for NVH simulations. In this method, firstly the most influential parameters are determined using a SA to reduce the number of input parameters. Depending on the number of parameters and the computation time of the NVH simulation model, either the Morris SA or an EFAST SA is chosen. Finally, a fuzzy UA is performed, which quantifies the uncertainty of the output of the NVH simulation and provides its possible ranges. The procedure is applied to the NVH model for predicting air borne sound of an electric drive with 53 uncertain input parameters.