Poly(ethylene glycol) methyl ether (PEG)-poly(${eta}$-amino ester) (PAE) block copolymers were synthesized using a Michael-type step polymerization, and the construction of pH-sensitive polymeric micelles (PM) investigated. The ${eta}$-amino ester block of the block copolymers functioned as a pH-sensitive moiety as well as a hydrophobic block in relation to the ionization of PAE, while PEG acted as a hydrophilic block, regardless of ionization. The synthesized polymers were characterized using $^1H-NMR$, with their molecular weights measured using gel permeation chromatography. The $pK_b$ values of the pH-sensitive polymers were measured using a titration method. The pH-sensitivity and critical micelle concentration (CMC) of the block copolymers in PBS solution were estimated using fluorescence spectroscopy. The pH dependent micellization behaviors with various bisacrylate esters varied within a narrow pH range. The critical micelle concentration at pH 7.4 decreased from 0.032 to 0.004 mg/mL on increasing the number of methyl group in the bisacrylate from 4 to 10. Also, the particle size of the block copolymer micelles was determined using dynamic light scattering (DLS). The DLS results revealed the micelles had an average size below 100 nm. These pH-sensitive polymeric micelles may be good carriers for the delivery of an anticancer drug.