An estimation device for a cylinder intake air amount and an internal EGR rate in an internal combustion engine is provided which is capable of making an estimation with a high degree of accuracy in a small number of adaptation constants. The estimation device calculates a volumetric efficiency corresponding value and the internal EGR rate based on an exhaust efficiency (a linear function of intake pipe internal pressure) which is an index indicating an amount of residual gas which is an exhaust gas after combustion remaining in the cylinder without being discharged from the cylinder to an exhaust pipe, and an intake efficiency (a linear function of intake pipe internal pressure) which is an index indicating an amount of air coming into the cylinder from the intake pipe excluding the residual gas.