Discussion of consumer behavior is important to the economy, particularly in the Islamic economy. In this paper intertemporal consumption theory in the Islamic economic framework has been developed. Beginning, according to the Hadith and the framework of intertemporal consumption theory, it was concluded that the utility function of individual Muslims in addition of consumption depend on the charity. According to the budget constraints of individual Muslim, one fifth of the savings should be paid in khoms (1/5 of Savings). In this paper khoms is intended. Most orders in Islam exist that prevent of excesses and wastage. We optimized utility function according to budget constraint for the individual Muslims. After solving the model and according to the obtained equations, the optimal path of consumption and optimal path of charity are plotted over the time. Optimal routes based on the values ​​of zero interest rates and interest rates of 1% is plotted. Result was obtained with a zero interest rate that optimal consumption will be constant over time. According to the equations that calculated, consumption and charity in any given time dependent only to the present value of lifetime income and don’t dependent to the other variables such as prior consumption or charity. Also Note that the optimal consumption path is independent of the charity and also the optimal path of charity is independent of the consumption. The optimal paths of consumption and the charity only dependent to present value of income. With analysis on the present value of income variable have showed that the increase in total income only move up the optimal path of consumption and charity and does not change slope of path. All graphs in this study plotted with Matlab software.