Based on our previous work about a co-evolution of massive black holes (MBH) and their host spheroids, we estimate the cosmic star formation history associated with AGN accretion by ROSAT X-ray All sky surveys. We show: 1) the total amount of star formation associated with MBH growth is at least half of the net star formation at high redshift, which probably totally missed by the current UV/optical deep surveys; 2) the FIR emission from the dust heated by star formation on-going during the MBH growth could be a significant energy source for SCUBA populations; 3)the peak redshift of the massive spheroid formation in this case is around 1.5, not necessary to be at much higher redshift.