Chemical Species Tomography (CST) has been widely applied for imaging of critical gas-phase parameters in industrial processes. To acquire high-fidelity images, CST is typically implemented by line-of-sight Wavelength Modulation Spectroscopy (WMS) measurements from multiple laser beams. The modulated transmission signal on each laser beam needs to be a) digitised by a high-speed analogue-to-digital converter (ADC); b) demodulated by a digital lock-in (DLI) module; and c) transferred to high-level processor for image reconstruction. Although a fully parallel data acquisition (DAQ) and signal processing system can achieve these functionalities with maximised temporal response, it leads to a highly complex, expensive and power-consuming instrumentation system with high potential for inconsistency between the sampled beams due to the electronics alone. In addition, the huge amount of spectral data sampled in parallel significantly burdens the communication process in industrial applications where in situ signal digitisation is distanced from the high-level data processing. To address these issues, a quasi-parallel sensing technique and electronic circuits were developed for industrial CST, in which the digitisation and demodulation of the multi-beam transmission signals are multiplexed over the high-frequency modulation within a wavelength scan. Our development not only maintains the temporal response of the fully parallel sensing scheme, but also facilitates the cost-effective implementation of industrial CST with very low complexity and reduced load on data transfer. The proposed technique is analytically proven, numerically examined by noise-contaminated CST simulations, and experimentally validated using a lab-scale CST system with 32 laser beams.