For grid-connected renewable energy equipment, asymmetrical high voltage swell threatens the grid-side converter (GSC) and the dc-link capacitor. Asymmetrical high voltage swell may cause significant fluctuations across the dc-link voltage, and energy reflux of the GSC, even result in the runaway of the GSC. To cope with this situation, the control strategy of the GSC has to be improved. Firstly, the controllability of the GSC is analyzed considering the asymmetrical high voltage swell situation and the converter power rating. Afterwards, an asymmetrical high voltage ride through (HVRT) control strategy is proposed by considering the reactive current compensation and the dc-link voltage fluctuations, which needs to raise the dc-link voltage in certain cases. However, increasing the dc-link voltage sometimes is not practical for the rating of the physical devices and the product cost. Therefore, the asymmetrical HVRT grid code has to be formulated carefully considering the operation capability of the GSC. The simulation experiments verified that the GSC can be controllable and the dc-link voltage is stable.