The effect of magnetic field on the discotic nematic liquid crystalline polymers (LCPs) is analyzed with the extended Doi theory, in which the molecular shape parameter (β) is defined at −1.0. The evolution equation for the probability function of the discotic nematic LCP molecules is solved without any closure approximations. The transition among flow‐orientation modes, such as tumbling, wagging, and aligning defined similar to the rodlike LCPs, is strongly affected by the magnetic fields. The new aligning flow‐orientation mode observed for the rodlike LCPs under magnetic fields also can be investigated in the lower shear rate region. On the other hand, the effect of magnetic fields parallel to the x‐ and y‐axis on the time‐averaged first and second normal stress differences ( $\bar N_1^*$, $\bar N_2^*$) are also studied. It can be seen that the shear rate regions of the sign changes of $\bar N_1^*$, $\bar N_2^*$ are completely contrary to those conclusions achieved for the rodlike LCPs. In addition, the absolute values of $\bar \eta ^*$ increase with the magnetic field strength in the lower shear rate range owing to the new aligning flow‐orientation mode. Finally, the flow‐phase diagram versus β is also discussed. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013