Image registration is an elementary task in medical image processing and analysis, which can be divided into monomodal and multimodal. Direct 3D multimodal registration in volumetric medical images can provide more insight into the interpretation of subsequent image processing applications than 2D methods. This paper is dedicated to the development of a 3D multimodal image registration algorithm based on a viscous fluid model associated with the Bhattacharyya distance. In our approach, a modified Navier-Stoke's equation is exploited as the foundation of the multimodal image registration framework. The hopscotch method is numerically implemented to solve the velocity field, whose values at the explicit locations are first computed and the values at the implicit positions are solved by transposition. The differential of the Bhattacharyya distance is incorporated into the body force function, which is the main driving force for deformation, to enable multimodal registration. A variety of simulated and real brain MR images were utilized to assess the proposed 3D multimodal image registration system. Preliminary experimental results indicated that our algorithm produced high registration accuracy in various registration scenarios and outperformed other competing methods in many multimodal image registration tasks.Clinical Relevance- This facilitates the disease diagnosis and treatment planning that requires accurate 3D multimodal image registration without massive image data and extensive training regardless of the imaging modality.