Employing electron spin instead of charge to develop spintronic devices holds the merits of low-power consumption in information technologies. Meanwhile, the demand for increasing speed in spintronics beyond current CMOS technology has further triggered intensive researches for ultrafast control of spins even up to unprecedent terahertz regime. The femtosecond laser has been emerging as a potential technique to generate an ultrafast spin-current burst for magnetization manipulation. However, there is a great challenge to establish all-optical control and monitor of the femtosecond transient spin current. Deep insights into the physics and mechanism are extremely essential for the technique. Here, we demonstrate coherently nonthermal excitation of femtosecond spin-charge current conversion parallel to the magnetization in W/CoFeB/Pt heterostructures driven by linearly polarized femtosecond laser pulses. Through systematical investigation we observe the terahertz emission polarization depends on both the magnetization direction and structural asymmetry. We attribute this phenomenon of the terahertz generation parallel to the magnetization induced by linearly polarized femtosecond laser pulses probably to inverse spin-orbit torque effect. Our work not only is beneficial to the deep understanding of spin-charge conversion and spin transportation, but also helps develop novel on-chip terahertz opto-spintronic devices.