In this paper, we propose an effective scheme to create a frequency entangled states based on bound-to-bound inter-subband transitions in an asymmetric three-coupled quantum well structure. A four-subband cascade configuration quantum well structure is illuminated with a pulsed probe field and two continuous wave control laser fields to generate a mixing field. By properly adjusting the frequency detunings and the intensity of coupling fields, the conversion efficiency can reach 100%. A maximum entangled state can be achieved by selecting a proper length of the sample. We also numerically investigate the propagation dynamics of the probe pulse and mixing pulse, the results show that two frequency components are able to exchange energy through a four-wave mixing process. Moreover, by considering special coupling fields, the storage and retrieval of the probe pulse is also numerically simulated.