The modulus of elasticity of concrete (Ec) is an essential parameter commonly used in concrete design, concrete curing monitoring, and deterioration evaluation and damage detection of concrete structures. A quick and reliable in situ determination of Ec helps in accurate decision-making for construction and maintenance. The electromechanical impedance (EMI) technique using surface-bonded lead zirconate titanate (PZT) patches (referred to as SBP) has become a popular nondestructive method for monitoring concrete structures due to ease of operations. The existing research mainly utilized baseline-dependent approaches to monitor the changes (e.g., hardening or damage evolution) of concrete structures. However, relevant baselines are greatly influenced by the status of PZT sensors and bonding layers, limiting the practical applications of this technique. This paper presents a baseline-free EMI resonance method for measuring Ec of concrete without using prior baseline data for the first time. Numerical and experimental studies on standard concrete cubes (100 mm in width) with SBP were conducted to examine the proposed method. A dimensionless physical quantity was first proposed to view the EMI signals. Then, resonance peaks highly related to concrete properties but insensitive to the status of the sensor system were selected, physically described, and correlated to the concrete parameters through numerical analyses. Finally, experimental validations, covering the measurement of Ec, repeatability of the chosen resonance peaks, and temperature effects, were conducted to illustrate the proposed method’s stability, accuracy, and sensitivity.