[Problems]To provide a spherical aluminum nitride powder that features high thermal conductivity and filling property, and that is useful as a filler for a heat radiating material, and a method of producing the same.[Means for Solution]A spherical aluminum nitride powder comprising aluminum nitride particles having an average particle diameter of 3 to 30 μm, a sphericalness of not less than 0.75, and an oxygen content of not more than 1% by weight wherein, when the average particle diameter is d (μm), the specific surface area S (m2/g) satisfies the following formula (1), (1.84/d)≦S≦(1.84/d+0.5)  (1).