Evolution and fragmentation of a gas cloud are investigated for the primordial chemical composition which is the same as the products of the Big Bang. A pure-hydrogen gas cloud collapses isothermally at 500–1000 K when a low fraction of molecular hydrogen works as a coolant, and breaks into small subcondensations with mass less than 10 M⊙ due to thermal instability associated with molecular dissociation. On the other hand a pure-hydrogen gas cloud which contains no molecular hydrogen collapses isothermally at 6000–8000 K in a thermally stable condition, and enters the region where thermal energy exceeds radiation energy when thermal equilibrium between matter and radiation is achieved in the cloud. Consideration of energetics in the subsequent stage of the cloud evolution leads to the mass range of 0.1–20 M⊙ for the stable nuclear-burning protostars of the first generation. The thermal behavior of a gas cloud in the regime of z (the ratio of heavy element abundance to solar one) less than 10−4 is essentially similar to that in the case of no heavy element, and the heavy element cooling brings about thermal instability in a wide range of parameters in the regime of z greater than 10−3. Linear perturbation analysis gives growth time of the instability much shorter than the free-fall time, and suggests the efficient excitation of density fluctuation driven by thermal instability. Thus the possibility of the initial mass function relatively enhanced in massive star at early times is denied, and the slow rate of metal enrichment in the interstellar medium is suggested.