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Luminance information plays an important role in dictating the quality of a color image, and some existing color filter array (CFA) demosaicking methods achieve superiority by first reconstructing a satisfactory luminance plane. It is however difficult to accurately estimate the luminance from CFA samples since their color spectra are generally aliased. Extending a state-of-the-art luminance-based demosaicking scheme, in this paper we propose an improved demosaicking method using an efficient filter to estimate the luminance at green pixels and employing an effective edge-adaptive interpolation scheme to obtain the luminance at red and blue pixels. Experimental results demonstrate that not only is the proposed method less complex, it also performs noticeably better, both visually and in terms of peak signal-to-noise ratio, comparing with several recent methods.