The electrical characteristics of tissue yield valuable information for early diagnosis of pathological changes. Magneto-acoustic imaging is a functional approach for imaging of electrical conductivity. This study proposes a continuous-wave magneto-acoustic imaging method. A kHz-range continuous signal with an amplitude range of several volts is used to excite the magneto-acoustic signal and improve the signal-to-noise ratio. The magneto-acoustic signal amplitude and phase are measured to locate the acoustic source via lock-in technology. An optimisation algorithm incorporating nonlinear equations is used to reconstruct the magneto-acoustic source distribution based on the measured amplitude and phase at various frequencies. Validation simulations and experiments were performed in pork samples. The experimental and simulation results agreed well. While the excitation current was reduced to 10 mA, the acoustic signal magnitude increased up to 10-7 Pa. Experimental reconstruction of the pork tissue showed that the image resolution reached mm levels when the excitation signal was in the kHz range. The signal-to-noise ratio of the detected magneto-acoustic signal was improved by more than 25 dB at 5 kHz when compared to classical 1 MHz pulse excitation. The results reported here will aid further research into magneto-acoustic generation mechanisms and internal tissue conductivity imaging.