Three-phase active damping LCL-type grid-connected converters are usually used in distributed power generation systems. However, serious inrush current will be aroused when the grid-connected converter starts, especially in rectifier mode, if no effective control method is taken. The point of common coupling (PCC) voltage feedforward is usually used to suppress start-up inrush current. Unfortunately, it will introduce a positive feedback loop related to the grid current and grid impedance under weak grid conditions, and therefore, the grid current will be distorted and the system stability margin will be significantly reduced. To solve the above problems, this paper proposes a simple method based on a d-axis fundamental positive-sequence component of filter capacitor voltage feedforward, without extra sensors and software resources. With the proposed method, it is possible to suppress the start-up inrush current and maintain the grid current quality and system stability under weak grid conditions. The mechanism of start-up inrush current and the effectiveness of the method for inrush current suppression are analyzed in detail. Then, the influences of different feedforward methods on system stability are analyzed under weak grid conditions by the impedance model of grid-connected converter. Finally, experimental results verify the validity of the proposed method.