As a noninvasive neuromodulation technique, transcranial magnetic stimulation (TMS) has important applications both in the exploration of mental disorder causes and the treatment of mental disorders. During the stimulation, the TMS system generates the intracranial time-varying induced E-field (E-field), which alters the membrane potential of neurons and subsequently exerts neural regulatory effects. The temporal waveform of the induced E-fields is directly related to the stimulation effect. To meet the needs of scientific research on diversified stimulation waveforms and flexible adjustable stimulation parameters, a novel efficient pulse magnetic stimulation circuit (the EPMS circuit) design based on asymmetric cascaded multilevel technology is proposed in this paper. Based on the transient analysis of the discharge circuit, this circuit makes it possible to convert the physical quantity (the intracranial induced E-field) that needs to be measured after magnetic stimulation into easily analyzable electrical signals (the discharge voltage at both ends of the stimulation coil in the TMS circuit). This EPMS circuit can not only realize monophasic and biphasic cosine-shaped intracranial induced E-fields, which are widely used in the market, but also realize three types of new intracranial induced E-field stimulation waveform with optional amplitude and adjustable pulse width, including monophasic near-rectangular, biphasic near-rectangular and monophasic/biphasic ladder-shaped stimulation waveform, which breaks through the limitation of the stimulation waveform of traditional TMS systems. Among the new waveforms produced by the EPMS circuit, further research was conducted on the dynamic response characteristics of neurons under the stimulation of the biphasic four-level waveform (the BFL waveform) with controllable parameters. The relationship between TMS circuit parameters (discharge voltage level and duration) and corresponding neural response characteristics (neuron membrane potential change and neuronal polarizability ratio) was explained from a microscopic perspective. Accordingly, the biological physical quantities (neuronal membrane potential) that are difficult to measure can be transformed into easily analyzable electrical signals (the discharge voltage level and duration). Results showed that compared with monophasic and biphasic cosine induced E-fields with the same energy loss, the neuron polarization ratio is decreased by 54.5% and 87.5%, respectively, under the stimulation of BFL waveform, which could effectively enhance the neuromodulation effect and improve the stimulation selectivity.