Fractal river networks and the relationship between mainstream length and drainage area of Jilin Province are researched in the paper by means of new theoretical progress in fractal geomorphology. It has been proved that the parameter (α) based on Horton’s law, which is always expressed as α=lnR_b/lnR_l, is a fractal dimension in hierarchical sense instead of spatial sense, and  the double of the scaling factor(b) based on Hack's model,L=μA^b, which can be written as b=lnR_l/lnR_a, is not fractal dimension of river courses, but a ratio of generalized dimension of mainstream to that of corresponding catchment (the latter is not always equal to 2). A discovery is made that the α values of river networks in mountainous areas or rainy places are greater than those in flatlands or the areas with less rainfall, and the b values to the contrary. The contributing factors of the spatial patterns of α- and b- values of river systems distributing in Jilin's map are directed to the configuration of land surface, property of rocks, and precipitation, etc. One of the definition on fractal dimensions of river networks given by LaBarbera and Rosso,D=min(2,2logR_b/logR_a), has been revised as D=min［2,max(1,2logR_b/logR_a)］, according to the calculated results from the data of Jilin's rivers.