An important question in non life insurance research is the estimation of number of future payments and corresponding amount of them. A loss reserve is the money set aside by insurance companies to pay policyholders claims on their policies. The policyholder behavior for reporting claims after its occurrence have significant effect on the costs of the insurance company. This article considers the problem of predicting the amount and number of claims that have been incurred but not reported, say IBNR. Using the delay probabilities in monthly level, calculated by the Zero Inflated Gamma Mixture distribution, it predicts IBNR's loss reserve. The model advantage in the IBNR reserve is insurers can predict the number of future claims for each future date. This enables them to change the claim reporting process. The practical applications of our findings are applied against a third party liability (TPL) insurance loss portfolio. Additional information about claim can be considered in the loss reserving model and making the prediction of amount more accurate.