In this paper, we study the properties of positive solutions for the reaction-diffusion equation $u_t$ = $Delta_u+{int}_Omega u^pdx-ku^q$ in $Omega imes(0,T)$ with nonlocal nonlinear boundary condition u (x, t) = ${int}_{Omega}f(x,y)u^l(y,t)dy$ $partialOmega imes(0,T)$ and nonnegative initial data $u_0$ (x), where p, q, k, l > 0. Some conditions for the existence and nonexistence of global positive solutions are given.