Abstract: The network calculation of ²⁶Al nucleosynthesis in 3M_\odot AGB stars and the sensitivity analysis of nuclear reaction rates have been investigated in this article. After establishing a complete nuclear reaction network from carbon to silicon, combined with the latest nuclear reaction rate data, we have calculated the abundance of ²⁶Al. The results show that ²⁶Al is effectively synthesized in the AGB stars at the beginning, but as the reaction proceeding, ²⁶Al is consumed by a series of nuclear reactions. The MgAl cycle appears in the network of ²⁶Al. We divide the main nuclear reactions in the reaction network into three categories (n, \gamma ), (p, \gamma ) and (\alpha,\,\gamma ), and the sensitivity of nuclear reaction rates has been analyzed in detail. We have identified the most influential reactions in each type of nuclear reactions, they are: ²⁵Mg(n, \gamma )²⁶Mg, ²⁵Mg(p, \gamma )²⁶Al, ²⁶Mg(p, \gamma )²⁷Al, ²¹Ne(p, \gamma )²²Na, ¹⁸O(\alpha,\,\rm\gamma )²²Ne and ²²Ne(\alpha,\,\rm\gamma )²⁶Mg. Among all the nuclear reactions involved in the present network, ²⁵Mg(p, \rm\gamma )²⁶Al is the one that has the greatest impact on the yield of ²⁶Al, which deserves the attention of nuclear experimentalists.