We present the attenuated spline reconstruction technique (aSRT) which provides an innovative algorithm for single photon emission computed tomography (SPECT) image reconstruction. aSRT is based on an analytic formula of the inverse attenuated Radon transform. It involves the computation of the Hilbert transforms of the linear attenuation function and of two sinusoidal functions of the so-called attenuated sinogram. These computations are achieved by employing the attenuation information provided by computed tomography (CT) scans and by utilizing custom-made cubic spline interpolation. The purpose of this work is: (i) to present the mathematics of aSRT, (ii) to reconstruct simulated and real SPECT/CT data using aSRT and (iii) to evaluate aSRT by comparing it to filtered backprojection (FBP) and to ordered subsets expectation minimization (OSEM) reconstruction algorithms. Simulation studies were performed by using an image quality phantom and an appropriate attenuation map. Reconstructed images were generated for 45, 90 and 180 views over 360 degrees with 20 realizations and involved Poisson noise of three different levels (NL), namely 100% (NL1), 50% (NL2) and 10% (NL3) of the total counts, respectively. Moreover, real attenuated SPECT sinograms were reconstructed from a real study of a Jaszczak phantom, as well as from a real clinical myocardial SPECT/CT study. Comparisons between aSRT, FBP and OSEM reconstructions were performed using contrast, bias and image roughness. The results suggest that aSRT can efficiently produce accurate attenuation-corrected reconstructions for simulated and real phantoms, as well as for clinical data. In particular, in the case of the clinical myocardial study, aSRT produced reconstructions with higher cold contrast than both FBP and OSEM. aSRT, by incorporating the attenuation correction within itself, may provide an improved alternative to FBP. This is particularly promising for ‘cold’ regions as those occurring in myocardial ischaemia.