A theory of the c-axis infrared conductivity of a dx2-y2 -wave superconductor due to the competition betweenthe interlayer direct hopping and the hopping assisted by the spin fluctuations has been developed. The prediction ofourtheory captures the main feature of the experiment. Thus we argue that the anomalous behavior of the c-axis infraredconductivity of the underdoped cuprates in superconducting state may be properly understood within the theory.