Rapid and non-destructive detection of invisible handwriting, such as erasure, steganography and covering, is a research difficulty in the field of forensic scientific document inspection. In the current research, the method of switching multi-band light source and filter is mostly used to visualise the invisible handwriting, but the spectroscopy mechanism of invisible handwriting is less analyzed. Therefore, the efficiency of invisible handwriting and the success rate of testing are both not high. In order to improve the efficiency and accuracy of erasure, steganography and covering in document examination, the mechanism and rapid visualization method of the three kinds of invisible handwriting were studied by measuring the excitation and fluorescence spectra, reflection and transmission spectra, and micro-topography. Based on the hyperspectral imaging technology of liquid crystal tunable filter (LCTF) and support vector machine (SVM) classification algorithm, a rapid test method for simultaneous display and classification of invisible handwriting is proposed. Chenguang and Pilot erasable pen, fluorescent writing pen and lemon juice emit strong fluorescence under the excitation of 365 nm long-wave ultraviolet light. The fluorescence wavelength of erasable pen and lemon juice is about 716 nm, and the fluorescence wavelength of fluorescent writing pen is 447 nm. Besides the lemon juice invisible writing can also be effectively visualized by using 254 or 365 nm ultraviolet reflection imaging. In the study of covering handwriting, it is found that the transmittance of a ballpoint pen, marker pen and erasable pen is more than 60% in the infrared band of 700~2 500 nm, and the transmittance of a gel pen is less than 20%. Therefore, the near-infrared band of 850 nm imaging is used to effectively visualize the Chenguang gel pen covered by a Pilot ballpoint pen. The LCTF hyperspectral camera was used to image the three kinds of invisible handwriting in the range of 400~720 nm with a step of 5 nm, and the different handwriting in the image were visualized classified simultaneously by SVM classification algorithm, the total classification accuracy was 99.284 4%, and the Kappa coefficient was 0.959 1. Photoluminescence imaging using a 365 nm light source as an excitation light can effectively visualize erasure and steganography handwriting. Because the reflectivity of different inks in the near-infrared band is quite different, near-infrared imaging can effectively visualize the covering handwriting. SVM classification technology based on LCTF hyperspectral imaging can realize the simultaneous display and classification of different types of invisible handwriting and has high visualization efficiency and classification accuracy.