We present a new approach to the quantization of free electromagnetic fields without the infinity problem.Our work shows that from the physical viewpoint, the energy of a free electromagnetic field in a finite volume should be represented necessarily by a finite series, since fields consist of a finite number of photon.From the mathematical viewpoint, it is explained that the quantization of electromagnetic field reduces the infinite Fourier series to a finite series and preserve the relativistic invariance.It is demonstrated that the cut-off of series for the energy of photons is uniquely and objectively determined based on the assumption about photon.Based on this perspective, the interaction between free electromagnetic field and matter is described in terms of an integral in a finite interval which does not comprise zero and infinity.Our methodology always gives finite results and thus does not need renormalization.Ultimately, it is demonstrated that it is possible to construct a new quantization theory of electromagnetic field without infinity and renormalization thereof.