It has been reported that highly adsorptive granular activated carbon improves the biofilter performance. In this work the effect of adsorption property of the medium,on the biofilter capacity of eliminating organic components in waste gas streams is theoretically discussed using a biofilter model. In this first paper adsorption capacity is assumed to be in excess and steady-state solutions are compared with Ottengraf's solutions in various limiting situations. When first-order kinetics is used in the substrate utilization rate, as the value of alpha increases, the corresponding values of the dimensionless pollutant concentration in a biofilm and the dimensionless pollutant concentration in waste-gas streams through a biofilter become lower at a given value of Thiele modulus, through the thickness of the biofilm and the height of the biofilter, respectively. However, the effect of alpha becomes insignificant when the value of Thiele modulus becomes larger than a certain number. With zero order kinetics in the substrate utilization rate, for both situations of reaction limiting and diffusion limiting, their steady-state solutions are obtained.