The uncertain nature and variability in solar power generation requires the development of methods to further improve the solar forecasting, specifically in very short term to drive the system operational decisions. With regard to this issue, this paper provides an innovative approach for predicting solar power in very short term using a Suboptimal Multiple Fading Extended Kalman Filter (SMFEKF). In this method, the fading factors are adjusted dynamically resulting in the SMFEKF having reduced computational burden as compared to traditional Kalman Filters such as Uncented Kalman Filter (UKF) and Extended Kalman Filter (EKF). Improving estimation precision is achieved through dynamically updating the covariance of process noise and measurement noise. In the proposed method, the historical solar irradiance data, numerical weather predictions, and the real-time power measurements are used to optimize prediction precision. The proposed SMFEKF demonstrates slightly better accuracy but significantly reduced computational burden and time.