We investigate a method to construct parametrized progenitor models for core-collapse supernova simulations. Different from all modern core-collapse supernova studies, which rely on progenitor models from stellar evolution calculations, we follow the methodology of Baron & Cooperstein (1990) to construct initial models. Choosing parametrized spatial distributions of entropy and electron fraction as a function of mass coordinate and solving the equation of hydrostatic equilibrium, we obtain the initial density structures of our progenitor models. First, we calculate structures with parameters fitting broadly the evolutionary model s11.2 of Woosley et al. (2002). We then demonstrate the reliability of our method by performing general relativistic hydrodynamic simulations in spherical symmetry with the isotropic diffusion source approximation to solve the neutrino transport. Our comprehensive parameter study shows that initial models with a small central entropy ($lesssim 0.4,k_B$ nucleon$^{-1}$) can explode even in spherically symmetric simulations. Models with a large entropy ($gtrsim 6,k_B$ nucleon$^{-1}$) in the Si/O layer have a rather large explosion energy ($sim 4times 10^{50}$ erg) at the end of the simulations, which is still rapidly increasing.
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