The uncertainties of spot size and position need to be clarified for x-ray sources as they can affect the detecting precision of the x-ray probe beam in applications such as radiography. In particular, for laser-driven x-ray sources, they would be more significant as they influence the inevitable fluctuation of the driving laser pulses. Here, we have employed the penumberal coded aperture imaging technique to diagnose the two-dimensional spatial distribution of an x-ray emission source spot generated from a Cu solid target irradiated by an intense laser pulse. Taking advantage of the high detection efficiency and high spatial resolution of this technique, the x-ray source spot is characterized with a relative error of ∼5% in the full width at half maximum of the intensity profile in a single-shot mode for general laser parameters, which makes it possible to reveal the information of the unfixed spot size and position precisely. Our results show the necessity and feasibility of monitoring the spot of these novel laser-driven x-ray sources via the penumbral coded aperture imaging technique.