In this paper , we use the Type Ia supernova data as well as the CMB and LSS data to constrain the agegraphic dark energy model recently proposed by Cai . Due to its peculiar nature , the parameter n of this model can not be well constrained by the SNIa data , while the other parameter \Omega _ { m 0 } can be constrained to be 0.34 \pm 0.04 . When combined with CMB and LSS data , the range of 1 \sigma confidence level for n is greatly narrowed , albeit still very large . The best fit result is \Omega _ { m 0 } = 0.28 \pm 0.02 , which is consistent with most observations like WMAP and SDSS , and n = 3.4 , of which a meaningful range of confidence level can not be obtained due to the fact that the contours are not closed . Despite of this result , we conclude that for n > 1 this model is consistent with SNIa , CMB and LSS observations . Furthermore , the fitting results indicate a generalized definition for the agegraphic dark energy .