Longitudinal acceptance of the Spallation Neutron Source superconducting linac is computed with a longitudinal model. Beam Current Monitor and Beam Loss Monitors are utilized in the beam acceptance measurements, and the measured results show close agreement with the model. Based on the simulations and on the measurements of the acceptance of the superconducting linac, we developed a novel method to measure beam bunch shape, beam energy profile and the longitudinal emittance at the entrance of the linac. The experiment measurements reveal that a large longitudinal beam halo exists in the injection beams to the superconducting linac, and the longitudinal emittance is approximately twice that of the nominal design. The simple measurement method is applicable to other linacs.