The autonomous navigation of a micro aerial vehicle (MAV) relies faithfully on the capacity of the localization and the building map of the explored environment. This hard task is known as simultaneous localization and mapping (SLAM). To overcome this problem, many approaches have been proposed based on a variety of sensors. The most popular are those based on monocular vision. But practically all the monocular SLAMs (Mono SLAM) suffer from the scale drift due to the difficulty of depth estimation. To avoid this limitation, the use of a second sensor is crucial to retrieving a metric pose to navigate safely. The Mono-SLAM problem has been resolved by many authors as a problem of filtering or optimization. In this paper, we propose a new SLAM scheme based on a robust filter named Smooth Variable Structure Filter (SVSF). The main advantage of our solution compared to previous solutions is the use of an Inertial Measurement Unit (IMU) associated with a single camera. The different results of the IMU-Mono-SLAM obtained from simulation and experimentation on a well-known dataset prove the reliability, robustness, and accuracy of the proposed solution (SVSF-SLAM) compared to the classical approach (EKF-SLAM).