Abstract. We analyze the normal electronic states of Na 0.35 CoO 2 based on the multi-orbital Hubbard model using the FLEX approximation. The fundamental electronic property of this system is drastically changed by the presence or absence of the small hole pockets associated with the e ′ g orbital. This change of the Fermi surface topology may be caused by the crystalline electric splitting due to the trigonal distortion. When small hole pockets are absent, the weak pseudogap bahaviors appear in the density of states and the uniform spin susceptibility, which are observed by recent experiments. We estimate the mass enhancement factor of quasiparticle m * /m ≃ 1.5 ∼ 1.8. This result suppports ARPES measurements. . While many theretical and experimental studies are widely performed, the topology of Fermi surface (FS) and the low-energy electronic structure are still unresolved. To resolve these problems is very important to find out the mechanism of superconductivity.In Na x CoO 2 , local density approximation (LDA) calculations [2] have predicted that Na x CoO 2 has a large FS associated with the a 1g band and six small hole pockets corresponding to the e ′ g band. However, such small pockets are not observed in recent ARPES measurements [3,4]. ARPES measurements also observed that renomarized quasiparticle bandwidth is approximately half of that calculated by band calculation. In the present work, we study the normal electronic states in Na 0.35 CoO 2 using the fluctuation exchange (FLEX) approximation to elucidate Fermi surface topology and renormalized band structure. In Na x CoO 2 , the topology of the FS is sensitively changed by the a 1g -e ′ g splitting 3V t , whose value can be modified by the trigonal distortion of crystal. In this work, we study the many body effect for various values of 3V t .We have reported[5] that density of states (DOS) on the Fermi energy and uniform spin susceptibility increase as temperature decreases when small pockets exist. On the other hand, when small pockets are absent, both of them decrease at lower temperatures. It is a weak pseudogap behavior due to magnetic fluctuations. In this case, the degree of reduction of DOS is greater when the top of the e ′ g band is just below the Fermi level. In experimental measurements, both uniform spin susceptibility [6] and DOS in the photoemission spectroscpy [7] decrease at lower temperatures. These pseudogap behaviors are consistent with the latter result. As the pseudogap in the DOS is more prominent in bilayer hydrate samples than that in monolayer ones, the effect of intercalation of water is expected to raise the e ′ g band slightly as expected by the analysis based on the point charge model. As a result, we have concluded that the small Fermi pockets do not exist or very small if any.In this paper, we report the band structure of Na 0.35 CoO 2 at 3V t = 0.12. In this case, small hole pockets are absent; they sink just below the Fermi energy. We find that the quasiparticle band is renormalized by the electronic correlation, and m...