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In this paper, we present a novel integral transform known as the one-dimensional quaternion quadratic-phase Fourier transform (1D-QQPFT). We first define the one-dimensional quaternion quadratic-phase Fourier transform (1D-QQPFT) of integrable (and square integrable) functions on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="bold">R</mi></semantics></math></inline-formula>. Later on, we show that 1D-QQPFT satisfies all the respective properties such as inversion formula, linearity, Moyal’s formula, convolution theorem, correlation theorem and uncertainty principle. Moreover, we use the proposed transform to obtain an inversion formula for two-dimensional quaternion quadratic-phase Fourier transform. Finally, we highlight our paper with some possible applications.