The dynamic behaviors of a geometrically nonlinear oscillator with dry friction were studied by the event-driven method. Firstly， the geometrically nonlinear dry-friction oscillation system was modeled as a Filippov system. Then， the algorithm based on the event-driven method was introduced to solve the Filippov system with discrete vector field， which could accurately detect the entry and exit of the sliding motion area. Two different kinds of Poincare cross section were used to reveal the transformation process between different types of periodic motions with sliding process as parameters change. Finally， different types of sliding bifurcation and periodic doubling bifurcation were studied， and the existence of multiple sliding segments in the doubling process was found.