Hjort(1990) obtained the nonparametric Bayes estimator $^{F}_{c,a}$ of $F_0$ with respect to beta processes in the random censorship model. Let $X_1,{cdots},X_n$ be i.i.d. $F_0$ and let $C_1,{cdot},;C_n$ be i.i.d. G. Assume that $F_0$ and G are continuous. This paper shows that {$^{F}_{c,a}$(u){|}0 < u < T} converges weakly to a Gaussian process whenever T < $infty$ and $~{F}_0({ au});<;1$.