One brand new cement-based magnetoelectric (ME) composite with its outstanding performance has initiated new directions for updated sensor development and monitoring applications in civil engineering. On the premise of applying the preferred processing method and laminated connectivity concluded before, the sandwich structured cement-based ME composites with different thickness ratios of the magnetostrictive layers to the piezoelectric layer have been developed to analyze the dominant influence factors on the key properties of the composites in this investigation. The contrastive results show that the piezoelectric factor and acoustic impedance of this laminated ME composite with the same type lead zirconate titanate (PZT) material present stable independence on the thickness ratios corresponding to the composition proportions. However, the important ME property of composites is strongly dependent on the applied field frequency, magnetic field H_dc and H_ac, the PZT layer thickness and the relative field orientation. At 1 kHz, the maximum ME response α_E31 of 1315 mV/cm·Oe for the ME composite with the intermediate PZT thickness of 0.8 mm was obtained. This strong ME response can be considered as the best ME performance ever found, which is superior to that of polymer-based composites reported. Moreover, it is worth to mention that the ME composites under different relative directions (vertical or parallel) of the magnetic field to the polarization orientation of PZT layer demonstrate greatly different ME coupling behaviors. Finally, it can be inferred the desirable properties of ME composites could be obtained by purposely choose the optimal volume fractions of different phases or other decisive parameters for accommodating various practical applications.