Single-pixel imaging (SPI), which uses a photodetector to detect the reflected total light intensity of a set of structured illumination patterns modulated by a target scene, provides a method for visible waveband imaging, hyperspectral imaging, and terahertz imaging. However, it faces a challenge when the scene to be imaged has specular reflections. To deal with this problem, a multi-angle method without feature matching is presented. With this method, the location of the detector does not affect image reconstruction, and the results of reconstruction at each location are matched at the pixel level automatically. In simulations, with the original image as a reference, the structural similarity index value of the picture obtained by the proposed method is 10% higher than the picture obtained from a single angle. The signal-to-noise ratio value of the picture obtained by the proposed method is 4.424, which is higher than 1.577 of the maximum value of the reconstruction result from a single angle. To evaluate the method, a metal key and an aircraft engine blade with specular reflections are taken as the target scene and are reconstructed from four different imaging perspectives, giving results that are matched at the pixel level. The final reconstructed image is obtained using the principal component analysis algorithm or the fourth-order partial differential equations and principal component analysis algorithm. Compared with the image obtained from a single angle, the correlation coefficient between the image obtained by the proposed method and the reference image is increased from the minimum value of 0.3139 to 0.7050, and the power ratio is increased from 4.52% to 73.63%. The proposed method has great potential specifically for improving the quality of SPI for scenes exhibiting specular reflections.