Most research on transient electromagnetic phenomena in the field of airborne electromagnetics focuses on three-dimensional isotropic media, with limited studies on anisotropy. Interpreting data from regions with significant electrical anisotropy using isotropic models can lead to significant deviations from reality. To analyze the impact and extent of electrical anisotropy on transient electromagnetic signals from long conductive sources, this study employs a finite volume-based three-dimensional forward modeling algorithm for arbitrary anisotropic media. By solving the discretized full tensor conductivity time-domain electromagnetic field equations, a methodology is developed. First, based on Maxwell's equations, and employing the background and anomaly separation theory, the computational domain is divided into a homogeneous half-space and an anomalous body. The electromagnetic response of the homogeneous half-space serves as the background field, while the electromagnetic response of the anomalous body forms the anomaly field. The curl equation of the electric field anomaly is further curled to obtain the curl equation for the secondary electric field. Integrating the curl equation for the secondary electric field within a control volume yields an integral equation. Applying Gauss's theorem converts the volume integral equation into a surface integral equation, which is then discretized for independent computation on the surface. Employing backward Euler algorithm in the time domain leads to the final discrete equation.To enhance accuracy and efficiency of time-domain electromagnetic field solution, the algorithm combines time segmentation with direct equation solving. The algorithm's validity is verified through one-dimensional anisotropic layered model calculations. Subsequently, the impact of principal axis anisotropy on attenuation voltage is simulated and analyzed. Arbitrary anisotropic models are then simulated and the effects of anisotropic dip and azimuth angles on the response are investigated. Finally, the algorithm's simulation capabilities for complex geological models are tested. Experimental results demonstrate the algorithm's effectiveness in three-dimensional arbitrary anisotropic forward modeling of transient electromagnetic phenomena, offering high precision in simulation outcomes.