The thermal conductivities κ of wurtzite InGaN are investigated using equilibrium molecular dynamics (MD) method. The κ of InGaN rapidly declines from InN (κ = 141 W/mK) or GaN (κ = 500 W/mK) to InGaN (x ≠ or 1), and reaches a minimum (κ = 19 W/mK) when × is around 0.5 at 300 K. The mean free path (MFP) of InGaN, ranging from 2 to 5 nm and following the same trend with the κ, is extrapolated in our simulation and a parabolic relationship between × and MFP is established. We find that the κ of InGaN decreases with increasing temperatures. The evolution of κ of InGaN is also examined by projecting the momentum-energy relationship of phonons from MD trajectories. The phonon dispersion and phonon density of states for InGaN reflect a slightly more flattened dispersive phononic curve of the alloying system. Despite an overestimated κ than experimental values, our calculated κ at 300 K agrees well with the results obtained by solving Boltzmann transport equation and also has the same stoichiometric trend with the experimental data. Our study provides the coherent analysis of the effect of thickness, temperature and stoichiometric content on the thermal transport of InGaN which is helpful for the thermal management of InGaN based devices.