We report on the analysis of 34 years of photometric observations of the pulsating helium atmosphere white dwarf GD358. The complete data set includes archival data from 1982 to 2006, and 1195.2 hr of new observations from 2007 to 2016. From this data set, we extract 15 frequencies representing g-mode pulsation modes, adding 4 modes to the 11 modes known previously. We present evidence that these 15 modes are l = 1 modes, 13 of which belong to a consecutive sequence in radial overtone k. We perform a detailed asteroseismic analysis using models that include parameterized, complex, carbon and oxygen core composition profiles to fit the periods. Recent spectroscopic analyses place GD358 near the red edge of the DBV instability strip, at 24,000 +/- 500K and a log g of 7.8 +/- 0.08 dex. The surface gravity translates to a mass range of 0.455-0.540M(circle dot). Our best-fit model has a temperature of 23,650K and a mass of 0.5706M(circle dot). That is slightly more massive than what is suggested by the most recent spectroscopy. We find a pure helium layer mass of 10(-5.50), consistent with the result of previous studies and the outward diffusion of helium over time.