A generalized Bak-Sneppen model (BS model) of biological evolution with
interaction strength $\theta$ is introduced in d-dimensional space, where the "nearest neighbors" are chosen among the 2d neighbors of the extremal site, with the probabilities related to the sizes of the fitnesses. Simulations of one- and two-dimensional models are given. For given $\theta>0$, the model
can self-organize to a critical state, and the critical threshold f_c(\theta)$ decreases as $\theta$ increases. The exact gap equation depending on $\theta$ is presented, which reduces to the gap equation of BS model as $\theta$ tends to infinity. An exact equation for the critical exponent $\gamma(\theta)$ is also obtained. Scaling relations are established among the six critical exponents of the avalanches of the model.