IN THIS PAPER WE INTRODUCE THE GENERALIZED INVERSE WEIBULL-GEOMETRIC (GIWG) DISTRIBUTION, WHICH IS OBTAINED BY COMPOUNDING GENERALIZED INVERSE WEIBULL AND GEOMETRIC DISTRIBUTIONS. THIS NEW DISTRIBUTION CONTAINS SEVERAL LIFETIME MODELS SUCH AS: INVERSE WEIBULL-GEOMETRIC (IWG), GENERALIZED INVERSE RAYLEIGHGEOMETRIC (GIRG) AND INVERSE RAYLEIGH-GEOMETRIC (IRG) DISTRIBUTIONS AS SPECIAL CASES.THE HAZARD RATE FUNCTION OF THE GIWG DISTRIBUTION CAN BE DECREASING AND UNIMODAL AMONG OTHERS.WE OBTAIN SEVERAL PROPERTIES OF THE GIWG DISTRIBUTION SUCH AS MOMENTS, MAXIMUM LIKELIHOOD ESTIMATION PROCEDURE VIA AN EM ALGORITHM AND INFERENCE FOR A LARGE SAMPLE. SUBMODELS OF THE GIWG DISTRIBUTION ARE STUDIED IN SOME DETAIL. IN THE END, APPLICATION TO A REAL DATA SET IS GIVEN TO SHOW THE EXIBILITY AND POTENTIALITY OF THE NEW DISTRIBUTION.