We studied InAs quantum dots (QDs) where electron Cooper pairs penetrate from an adjacent niobium (Nb) superconductor with the proximity effect. With time-resolved luminescence measurements at the wavelength around 1550 nm, we observed luminescence enhancement and reduction of luminescence decay time constants at temperature below the superconducting critical temperature (TC) of Nb. On the basis of these measurements, we propose a method to determine the contribution of Cooper-pair recombination in InAs QDs. We show that the luminescence enhancement measured below TC is well explained with our theory including Cooper-pair recombination.