Recently, imaging systems have exhibited remarkable image restoration performance through optimized optical systems and deep-learning-based models. Despite advancements in optical systems and models, severe performance degradation occurs when the predefined optical blur kernel differs from the actual kernel while restoring and upscaling the images. This is because super-resolution (SR) models assume that a blur kernel is predefined and known. To address this problem, various lenses could be stacked, and the SR model could be trained with all available optical blur kernels. However, infinite optical blur kernels exist in reality; thus, this task requires the complexity of the lens, substantial model training time, and hardware overhead. To resolve this issue by focusing on the SR models, we propose a kernel-attentive weight modulation memory network by adaptively modulating SR weights according to the shape of the optical blur kernel. The modulation layers are incorporated into the SR architecture and dynamically modulate the weights according to the blur level. Extensive experiments reveal that the proposed method improves peak signal-to-noise ratio performance, with an average gain of 0.83 dB for blurred and downsampled images. An experiment with a real-world blur dataset demonstrates that the proposed method can handle real-world scenarios.