L19-2 is a DAV star, which was intermittently observed from 1976 to 2013. Five independent pulsation modes of 350, 192, 143, 118, and 113 s are identified. The five modes can be used to constrain the fitting models. The rates of period change can be obtained through the O-C method for the modes of 192 and 113 s, which can be used to study the evolution effect of DAV stars. Using the White Dwarf Evolution Code (WDEC; 2018 version), a large sample of DAV star models are evolved. The theoretical modes are calculated and used to fit the observed modes. After fine model fittings, we obtain an optimal model with an absolute difference of phi = 0.06 s. By parameterizing the core oxygen profile, the WDEC procedure can greatly reduce the fitting error of asteroseismological models. According to our optimal model, the distance obtained through the model luminosity is only 1% different from that reported by the Gaia Data Release 2. L19-2 is a massive and hot DAV star with a relatively thick H atmosphere and a thick He layer. The stellar parameters and the rates of period change of our optimal model are slightly modified from that of the previous work. Our optimal model has a large central oxygen abundance. The central oxygen abundance is strongly correlated with the previous physical process of stellar evolution. A lot of asteroseismological work on white dwarfs presents an opportunity to explore the progenitor stars.