To realize accurate current control for a boost converter, a precise measurement of the inductor current is required to achieve high resolution current regulating. Current sensors are widely used to measure the inductor current. However, the current sensors and their processing circuits significantly contribute extra hardware cost, delay and noise to the system. They can also harm the system reliability. Therefore, current sensorless control techniques can bring cost effective and reliable solutions for various boost converter applications. According to the derived accurate model, which contains a number of parasitics, the boost converter is a nonlinear system. An Extended Kalman Filter (EKF) is proposed for inductor current estimation and output voltage filtering. With this approach, the system can have the same advantages as sensored current control mode. To implement EKF, the load value is necessary. However, the load may vary from time to time. This can lead to errors of current estimation and filtered output voltage. To solve this issue, a load variation elimination effect elimination (LVEE) module is added. In addition, a predictive average current controller is used to regulate the current. Compared with conventional voltage controlled system, the transient response is greatly improved since it only takes two switching cycles for the current to reach its reference. Finally, experimental results are presented to verify the stable operation and output tracking capability for large-signal transients of the proposed algorithm.