An optical multilayer film comprising a hard coat layer and a low refractive index layer of aerogel formed, in this order, directly or through a different layer on one surface of a basic material film containing transparent resin, and satisfying following expressions [1], [2] and [3], where nH is the refractive index of the hard coat layer and nL is the refractive index of the low refractive index layer. Expression [1]: nL =1.53 Expression [3]: √nH-0.2