Aluminum Gallium Nitride (AlGaN) nanofilms have been widely applied as active layers in ultra-violet (UV) opto-electronic devices and power electronics. Stress plays essential role in AlGaN based devices, especially in high electron mobility transistor (HEMT). Therefore, it is necessary to investigate the thermal properties of AlGaN nanofilms with various stresses. In this work, biaxial stressed [0001] oriented AlGaN nanofilms were studied. The phonon dispersion, density of states, velocity and heat capacity were simulated based on the elastic theory. Thermal conductivities of AlGaN nanofilms, which was found 1~2 orders of magnitude lower than the bulk materials, were then calculated by Boltzmann transport equation (BTE). Due to the modification of phonon dispersion and increasing of group velocity by tensile stress, the thermal conductivities of AlGaN nanofilms increase from compressive stress (-15 GPa) to tensile stress (+15 GPa). Moreover, a phonon energy gap appears in AlN nanofilm of -15 GPa, which disrupts the linear relation between thermal conductivity and stresses. Our work confirmed that the stress could be promising to tune the thermal conductivity of AlGaN nanofilms.