Usually, river patterns are greatly related to the natural factors, such as water erosion, landform, etc. Based on water erosion mechanism and original landform, a lattice model for river networks is proposed in order to simulate the growth process and to understand the selection of the nature, namely, fractal structure and scaling behaviors. The lattice is located at an inclined plane with fluctuant surface. The edges of the lattice are the possible water route. The selection of water route is dominated by the order of nature, that is, water flows downwards. A lattice point might be a "lake point", since its altitude is less than that of all the nearest neighbors. A steady river network might be set up as soon as all of the lake points disappear. Meanwhile, the scaling relationships dominating the fractal structure might be established. The statistical results on the landscape of the surface and the network connected by the water routes which actually mimic the river channels follow the Horton's laws. The laws suggest that the ratio of the average stream lengths of rank ω+1 to those of rank ω has a fixed value that is independent of ω. The same statements also hold for the ratios of average stream numbers and basin areas. The results show that the cumulative probabilities for the both stream lengths and basin areas conform to the power law distributions. These are in accord with those observed in the real river networks. These power laws indicate that there is no any characteristic scale in a river network. The spirit of the model shows that the dynamical origin of the scaling behavior might lie in both determinacy (erosion) and chance (fluctuations on the surface of the earth).