In this paper, a new mixed negative binomial (NB) distribution named as the negative binomial-weighted Garima (NB-WG) distribution is introduced for modeling count data. Two special cases of the formulation distribution, including negative binomial- Garima (NB-G), and negative binomial-size biased Garima (NB-SBG), are obtained by setting a specified parameter. Some statistical properties, such as the factorial moments, the first four moments, variance, skewness and kurtosis, have also been derived. Parameter estimation is done using maximum likelihood estimation (MLE), and real data sets are discussed to demonstrate the usefulness and applicability of the proposed distribution.