Abstract: Consider the two-sided truncation distribution families written in the form f(x,θ)=w(θ₁, θ₂)·h(x)I_[θ1,θ2](x)dx, where θ=(θ₁,θ₂). T(X)=(t₁(X), t₂(X))=(min(X₁, …, X_m), max(X₁, …, X_m)) is a sufficient statistic and we denote its marginal density by f(t)dμ^T. The prior distribution of θ belong to the famlly J={G:∫∫_Θ||θ||2dG(θ)<∞}. In this paper, we have constructed the empirical Bayes (EB) estimator of θ, φ_n(t), by using the kernel estimation of f(t) and established its convergence rates. Under suitable conditions it is shown that the rates of convergenc of EB estimator are O(N-^{((λk-1)(k+1))/(2(k+2)k))}, where the neural number k > 1 and 1/2 < λ < 1-(1/2k). Finally an example about this result is given.