Cosmic Microwave Background (CMB) is radiation that we receive from all directions of space. Most scientists believe that it is a radiant of the early universe. Its spectrum is equal to the spectrum of the blackbody in 2.725 K. We show that Quantum Redshift can describe CMB spectrum without the big bang and inflation theories. In the Quantum Redshift, at the emitting time, periods of the electromagnetic waves are not fully filled, and they are interested in absorbing quanta energies from younger periods. In this mechanism electromagnetic waves lose some periods while their quanta energies share with the remaining periods. Hence, their frequency will be decreased, and their spectrum will be converted to a lower equivalent temperature until their spectrum reaches the CMB spectrum. We anticipate our assay to be a starting point for a more sophisticated modeling universe. Predicting the age and size of the universe in a no expansion space is another usage of the Quantum CMB.