We report about the influence of nitrogen incorporation on the superconducting transition temperature T _C of TiNbMoTaW high entropy alloy films deposited using high power impulse magnetron sputtering. By measuring the temperature dependence of resistivity of (TiNbMoTaW)N _x nitrides, we observe a significant increase of T _C, from 0.62 K for x = 0 up to 5.02 K for x = 0.74. With further increase of x, T _C is decreasing and reaches 1.08 K for x = 0.97. The eightfold T _C enhancement seems to be associated with the incorporation of light N atoms into the face-centered cubic lattice and with the x dependent enhancement of the electron-phonon interaction, which may be related to the high configuration entropy in high entropy alloys. Measurements in magnetic field show that the upper critical fields B _c2 of (TiNbMoTaW)N _x with x > 0.15 provide B _c2/T _C > 2 T/K ratios, which are above the weak-coupling pair breaking limit. Additional heat capacity and point contact spectroscopy measurements show that the superconductivity in the ∼1 μm thick films is bulk in nature, consistent with conventional weak-coupling phonon mediated superconductivity. The proposed strategy of nitrogen incorporation into high entropy alloys may pave a pathway towards tailoring their superconducting properties, especially their T _C.