To extract channel characteristics and conduct channel modeling in millimeter-wave (mmWave) and Terahertz (THz) bands, accurate estimations of multi-path component (MPC) parameters in measured results are fundamental. However, due to high frequency and narrow antenna beams in mmWave and THz direction-scan measurements, existing channel parameter estimation algorithms are no longer effective. In this paper, a novel narrow-beam near-field space-alternating generalized expectation-maximization (N2-SAGE) algorithm is proposed, which is derived by carefully considering the features of mmWave and THz direction-scan measurement campaigns, such as near field propagation, narrow antenna beams as well as asynchronous measurements in different scanning directions. The delays of MPCs are calculated using spherical wave front (SWF), which depends on delay and angles of MPCs, resulting in a high-dimensional estimation problem. To overcome this, a novel two-phase estimation process is proposed, including a rough estimation phase and an accurate estimation phase. Moreover, considering the narrow antenna beams used for mmWave and THz direction-scan measurements, the usage of partial information alleviates influence of background noises. Additionally, the phases of MPCs in different scanning directions are treated as random variables, which are estimated and reused during the estimation process, making the algorithm immune to possible phase errors. Furthermore, performance of the proposed N2-SAGE algorithm is validated and compared with existing channel parameter estimation algorithms, based on simulations and measured data. Results show that the proposed N2-SAGE algorithm greatly outperforms existing channel parameter estimation algorithms in terms of estimation accuracy. By using the N2-SAGE algorithm, the channel is characterized more correctly and reasonably.