An image processing apparatus capable of making a user confirm effect of HDR reliably. An acquirer acquires a luminance component of an input image. A converter converts the luminance component acquired by the acquirer into a predetermined luminance value for each pixel. A generator generates a graph waveform image that shows a graph showing a distribution of the luminance values obtained through the conversion by the converter. A display controller displays the graph waveform image generated by the generator on a display unit. When the input image is recorded in a first mode, an axis representing the luminance values in the graph is a logarithmic axis, and the generator generates a logarithmic graph waveform image showing the distribution of the luminance values based on the logarithmic axis.