A new finite-element formulation, the high-speed GSMAC-FEM (generalized simplified marker and cell finite-element method), for incompressible viscous flow analysis is developed. The high-speed GSMAC-FEM is a stable and cost-efficient FEM method. The spatial discretization is simplified by a lumped mass matrix and 1-point quadrature. The wiggles are suppressed effectively by hourglass matrices and its effective coefficients which are adjusted to element shapes. Moreover, a new time marching algorithm which requires less effort to satisfy the continuity equation is applied. The time marching algorithm is an extension of the well-known HSMAC-FDM (highly simplified marker and cell finite difference method), and the algorithm runs more than twice as fast as the HSMAC time marching algorithm. The performance of the high-speed GSMAC-FEM scheme is examined by the analysis of the two-dimensional lid-driven cavity flow, and of the flow around circular cylinder. Last of all, one of the applications of the high-speed GSMAC-FEM with the k-ε turbulence model, i.e. the flow around a cube in a turbulent stream, is demonstrated.