Based on the framework of simultaneous localization and mapping (SLAM), SLAM with generalized objects (GO) has an additional structure to allow motion mode learning of generalized objects, and calculates a joint posterior over the robot, stationary objects and moving objects. While the feasibility of monocular SLAM has been demonstrated and undelayed initialization has been achieved using the inverse depth parametrization, it is still challenging to achieve unde-layed initialization in monocular SLAM with GO because of the delay decision of static and moving object classification. In this paper, we propose a simple yet effective static and moving object classification method using the velocity estimates directly from SLAM with GO. Compared to the existing approach in which the observations of a new/unclassified feature can not be used in state estimation, the proposed approach makes the uses of all observations without any delay to estimate the whole state vector of SLAM with GO. Both Monte Carlo simulations and real experimental results demonstrate the accuracy of the proposed classification algorithm and the estimates of monocular SLAM with GO.