Using measure theory, the concept of integration in the space of ordered Banach algebra was studied, using the measure space and the measurable function with values in ordered Banach algebra [7]. In this research, the concept of Daniell integration was presented without using measure theory so that some basic results were presented for functions with values in the space of ordered Banach algebra, we also defined the Daniell integral for the function with values in the ordered Banach algebra with the help of simple functions with values in the ordered Banach algebra and the upper and lower Daniell integral for functions with values in the ordered Banach algebra, with an explanation of some of the properties of this integration.
