Layer-dependent functional magnetic resonance imaging (fMRI) offers a compelling avenue for investigating directed functional connectivity (FC). To construct a comprehensive map of brain-wide directed FC, several technical criteria must be met, including sub-mm spatial resolution, adequate temporal resolution, functional sensitivity, global brain coverage, and high spatial specificity. Although gradient echo (GE)-based echo planar imaging (EPI) is commonly used for rapid fMRI acquisition, it faces significant challenges due to the draining-vein effect, particularly when utilizing blood oxygen level-dependent (BOLD) contrast. In this study, we mitigated this effect by incorporating velocity-nulling (VN) gradients into a GE-BOLD fMRI sequence, opting for a 3T magnetic field strength over 7T. We also integrated several advanced techniques, such as simultaneous multi-slice (SMS) acceleration and NORDIC denoising, to enhance temporal resolution, spatial coverage, and signal sensitivity. Collectively, the VN fMRI method exhibited notable spatial specificity, as evidenced by the identification of double-peak activation patterns within the primary motor cortex (M1) during a finger-tapping task. Additionally, the technique demonstrated BOLD sensitivity in the lateral geniculate nucleus (LGN). Furthermore, our VN fMRI technique displayed superior robustness when compared to conventional fMRI approaches across participants. Our findings of directed FC elucidate several layer-specific functional relationships between different brain regions and align closely with existing literature. Given the widespread availability of 3T scanners, this technical advancement has the potential for significant impact across multiple domains of neuroscience research.