This study proposes an efficient implicit computational framework, termed the absolute nodal coordinate–discrete-time transfer matrix method (ANC-DTTMM), for dynamic analysis of flexible slender beams undergoing large deformations and rotations. Building upon the absolute nodal coordinate formulation (ANCF) that inherently accounts for motion-deformation coupling effects, we derive the dynamic equations for three-node spatial beam elements. The integration of the Newmark scheme within the discrete-time transfer matrix method enables explicit expression of displacement and velocity variables through acceleration terms in nonlinear dynamic equations. The new version of the transfer matrix method is used to solve for the initial accelerations, and the explicit method is employed to perform preliminary estimation of the iterative initial values. This formulation permits the establishment of nonlinear algebraic equations at the element level, which are subsequently linearized into incremental form through Newton-Raphson iteration. The proposed methodology successfully constructs governing transfer equations and transfer matrices for large deformed flexible beam elements, facilitating systematic determination of full-field kinematic quantities along beam structures. Notably, this approach eliminates the need for assembling global system dynamic equations and computing Jacobian matrices at the system level. Numerical validation demonstrates the reliability and efficiency of the method in addressing geometrically nonlinear beam dynamics.