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In this paper we consider Abel equation $x' = g(t)x^2+f(t)x^3$, where $f$ and$g$ are analytical functions. We proved that if the equation has a center at$x=0$, then the Moment Conditions, i. e.,$m_k=\int_{-1}^1f(t)(G(t))^kdt=0,~~k=0,1,2$, is satisfied where$G(t)=\int_{-1}^tg(s)ds$. Besides, we give partial a positive answer to aconjecture proposed by Y. Lijun and T. Yun in 2001.

On Moment Condition and Center Condition for Abel Equation