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In this paper, we study the Gevrey regularity of spatially homogeneousBoltzmann equation without angular cutoff. We prove the propagation of Gevreyregularity for $C^\infty$ solutions with the Maxwellian decay to the Cauchyproblem of spatially homogeneous Boltzmann equation. The idea we use here isbased on the framework of Morimoto's recent paper (See Morimoto: J.Pseudo-Differ. Oper. Appl. (2010) 1: 139-159, DOI:10.1007/s11868-010-0008-z),but we extend the range of the index $\gamma$ satisfying $\gamma + 2s \in(-1,1)$, $s\in (0,1/2)$ and in this case we consider the kinetic factor in theform of $\Phi(v)=|v|^\gamma$ instead of $\la v \ra ^\gamma$ as Morimoto didbefore.

Gevrey regularity of spatially homogeneous Boltzmann equation without cutoff