In this paper,the asymptotic behavior of a non-local hyperbolic problem modelling Ohmic heating is studied.It is found that the behavior of the solution of the hyperbolic problem only has three cases:the solution is globally bounded and the unique steady state is globally asymptotically stable;the solution is infinite when t→∞;the solution blows up.If the solution blows up,the blow-up is uniform on any compact subsets of(0,1] and the blow-up rate is lim t → T*-u（x,t）（T*-t）1/α+βp-1=（α+βp-1/1-α）1/1-α-βp,where T* is the blow-up time.
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