The resonant transmission properties of a photonic quantum-well were studied by a spheric-wave expansion method in combination with multiple-scattering techniques. Similar to the electronic quantum wells the photonic quantum-well is constructed by sandwiching a uniform medium between two photonic barriers. The calculated resonant transmission peaks show that some photonic states exist in a quantized way, satisfying a quantized frequency relation. The finite photonic potential barrier plays different confining roles on the different photonic levels. By appropriately choosing the parameters of the well and barrier, a high-quality multichannel filtering can be achieved. The calculation in the coupled double photonic quantum-wells shows that the coupling between the modes in the two wells weakens with the widening of the barrier thickness, and the mode splitting becomes smaller.