Abstract: This paper studied the bounds of the tail probability of the sum of independent random variables with different negative binomial distributions. Firstly，under the condition of independent random variables with different negative binomial distributions，we used the probability generation function of the negative binomial distribution and Markov inequality to obtain tail probability bounds on the sum of random variables，which was improved to obtain a more accurate bound. Secondly，we obtained some bounds for the tail probability of the sum of negative dependent random variables by adding dependence relations under the condition of obeying the negative binomial distribution.

Key words: negative binomial distribution, negative dependence, tail probability