In clinical settings, computed tomography (CT), magnetic resonance imaging (MRI), or positron emission tomography (PET) are commonly employed in brain imaging to assist clinicians in determining the type of stroke in patients. However, these modalities are associated with potential hazards or limitations. In contrast, microwave imaging emerges as a promising technique, offering advantages such as non-ionizing radiation, low cost, lightweight, and portability. The primary challenges faced by microwave tomography include the severe ill-posedness of the electromagnetic inverse scattering problem and the time-consuming nature and unsatisfactory resolution of iterative quantitative algorithms. This paper proposes a learning electric field enhancement imaging method (LEFEIM) to achieve quantitative brain imaging based on a microwave tomography system. LEFEIM comprises two cascaded networks. The first, based on a convolutional neural network, utilizes the electric field from the receiving antenna to predict the electric field distribution within the imaging domain. The second network employs the electric field distribution as input to learn the dielectric constant distribution, thereby realizing quantitative brain imaging. Compared to the Born Iterative Method (BIM), LEFEIM significantly improves imaging time, while enhancing imaging quality and goodness-of-fit to a certain extent. Simultaneously, LEFEIM exhibits anti-noise capabilities.