25Al+p elastic scattering in inverse kinematics was measured to explore the level structure of 26Si above its proton threshold. The 2H(24Mg,n) 25Al reaction was used to produce a 3.4 MeV/nucleon 25Al radioactive beam with intensities of about 106 ions per second on target. By using a thick target of (CH2)n, a center-of-mass energy range of 3 MeV was scanned, reaching up to about 8.5 MeV in excitation energy in 26Si. This energy range covered the region of importance for the 25Al(p,γ)26Si at temperatures characteristic of explosive nucleosynthesis. Level parameters of six strong s-wave 25Al+p resonances in 26Si were extracted from fits to the measured excitation functions using the R-matrix formalism. Two new levels have been discovered, while for two others, our spin-parity assignments disagree with the results of some previous studies. Lastly, our resonance parameters for the remaining two levels are in good agreement with past experimental work, and with recent shell-model calculations.