To identify the anti-explosion performance, dynamic response and typical failure mode of a reinforced concrete beam-slab composite structure, the explosion experiment was conducted by the shock tube, which was used to simulate the long-lasting long-distance explosion shock wave. The failure form of the reinforced concrete beam-slab composite structure, the shock wave variation curve and the displacement change at the center point of the backside surface were obtained through the experiment. The dynamic response process of the reinforced concrete beam-slab composite structure is numerically simulated by finite element software. Compared with the experimental results, it is found that the simulated failure phenomenon is similar to the experimentally observed one, and the peak displacement at the center point of the backside surface is also close to the experimental one. Both of these have verified the accuracy and applicability of the numerical model adopted. On this basis, the dynamic response and failure process of the beam-slab composite structure under the simplified triangular explosion shock wave load are analyzed. The simplified triangular explosion shock wave used in numerical simulation has the same impulse as that in experiment but different peak values and durations. According to the deflection-span ratio a and the failure form, the failure patterns are classified into four modes as light failure, moderate failure, severe failure and complete failure. The results show that the cracks are firstly distributed along the diagonal of the backside surface of the reinforced concrete beam-slab composite structure. Under the same impulse, with the increase of the peak value of the explosion load, the damage degree of the beam-slab composite members gradually deepens. Meanwhile, the failure mode changes from a bending failure to a combined bending-shear failure, and finally appears as a punching failure. The failure of the plate part of composite members occurs earlier than the cross-beam part, while the former’s damage degree is greater than the latter’s.