We conduct numerical simulations of kerogen pyrolysis by the in situ upgrading process of Steamfrac, which entails the steam or hot-water injection into multistage transverse fractured horizontal well systems, by using a fully functional simulator developed to describe the in situ upgrading process. We first conduct simulation cases of a huff-n-puff method to analyze the sensitivity of temperature distribution of the reservoir to the positions of horizontal wells. Then, we conduct continuous hot-water injection and simultaneous fluid production cases, and analyze the productivity by applying two different irreducible saturations of aqueous phase in the rock matrix.