The three most iron-poor stars known until now are also known to have peculiar enhancements of intermediate mass elements. Under the assumption that these iron-deficient stars reveal the nucleosynthesis result of Pop III stars, we show that a weak supernova model successfully reproduces the observed abundance patterns. Moreover, we show that the initial parameters of the progenitor, such as the initial masses and the rotational property, can be constrained by the model, since the stellar yields result from the nucleosynthesis in the outer region of the star, which is significantly affected by the initial parameters. The initial parameter of Pop III stars is of prime importance for the theoretical study of the early universe. Future observation will increase the number of such carbon enhanced iron-deficient stars, and the same analysis on the stars may give valuable information for the Pop III stars that existed in our universe.