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In this paper, we investigate the extinction of solutions to a diffusion problem with a variable density as follows, (0.1) ρ(x)ut=Δum+ρ(x)u∫Ωupdx(x,t)∈Ω×[0,T),u(x,t)=0(x,t)∈∂Ω×[0,T),u(x,0)=u0(x)x∈Ω.We give some sufficient conditions for the extinction of solutions of (0.1) by using the method of comparison principle and the integral estimates.