Diffusion-limited aggregation (DLA) model is generalized to incorporate the dielectric breakdown model proposed by Niemeyer et al., and the new simulation method is proposed. While a growing cluster is still in the diffusion (Laplace) field, the local growth probability at a perimeter site Pps of the cluster is now given by pg(Pps) ∼|∇φ(Pps)|η, where Φ(P) is the probability of finding at a point P a random walker launched far away from the cluster. Ordinary DLA corresponds to η=1. Based on the theory of DLA proposed by Honda et al., the fractal dimension df for this generalized DLA is derived as [formula omitted], where ds is the dimension of space in which aggregation processes take place and dw is the fractal dimension of random walker trajectory. Both ds and dw are allowed to take any number larger than or equal to one. This formula is also applicable to Eden model (η=0) correctly, which means that the generalized DLA model naturally bridges a gap between ordinary DLA and Eden models.