Computational ghost holography is a single-pixel imaging technique that has garnered significant attention for its ability to simultaneously acquire both the amplitude and phase images of objects. Typically, single-pixel imaging schemes rely on real-value orthogonal bases, such as Hadamard, Fourier, and wavelet bases. In this Letter, we introduce a novel computational ghost holography scheme with Laguerre–Gaussian (LG) modes as the complex orthogonal basis. It is different from the traditional methods that require the number of imaging pixels to exactly match the number of modulation modes. Our method utilizes 4128 distinct LG modes for illumination. By employing the second-order correlation (SOC) and TVAL3 compressed sensing (CS) algorithms, we have successfully reconstructed the amplitude and phase images of complex objects, and the actual spatial resolution obtained by the experiments is about 70 µm. Due to the symmetry of the LG modes, objects with rotational symmetry can be recognized and imaged using fewer modes. The difference between bucket detection and zero-frequency detection is analyzed theoretically and verified experimentally. Moreover, in the process of object reconstruction, the advanced image processing function can be seamlessly integrated via the preprocessing of the LG modes. As such, it may find a wide range of applications in biomedical diagnostics and target recognition.