Delay and Sum (DAS) is one of the most common beamforming algorithms for photoacoustic imaging reconstruction that can function well in real-time imaging for its simplicity and quickness. However, high sidelobes and intense artifacts usually appear in the reconstructed image using DAS algorithm. To solve this problem, a novel beamforming algorithm called Multiple Delay and Sum with Enveloping (multi-DASE) is introduced in this paper, which can suppress sidelobes and artifacts efficiently. Compared to DAS, multi-DASE beamforming algorithm calculates not only the initial beamformed signal but also the N-shaped photoacoustic signal for each pixel. Firstly, Delay and Sum is performed multiply based on time series to recover the N-shaped photoacoustic signal for each pixel in the reconstructed image. And then, the recovered signal is enveloped to transform the N-shaped wave into a pulse wave to remove the negative part of the signal. Finally, signal suppression is performed on the enveloped signal which can lead to the suppression of sidelobes and artifacts in the reconstructed image. The multi-DASE beamforming algorithm was tested on the simulated data acquired with MATLAB k-Wave Toolbox. Experiment was also conducted to evaluate the efficiency of the multiDASE algorithm for clinical application. Both in computer simulation and experiment, our multi-DASE beamforming algorithm showed great performance in removing artifacts and improving image quality. In our multi-DASE beamforming algorithm, only fundamental operations and Discrete Fourier Transform (DFT) are performed, which means it can be a promising method for real-time clinical application.