Weak target detection is a great challenging in radar field. To detect the weak targets with beam migration, a novel tri-dimensional time model (i.e. fast time, slow time, and beam time) and a novel tri-dimensional signal model which based on the time model are set up firstly. Then, according to the presented models, we propose two multi-beam associated (MBA) coherent integration algorithms based on time-shared multi-beam (TSMB) and space-shared multi-beam (SSMB), respectively. The two proposed algorithms could both eliminate beam migration via associating multi-beam and realize coherent integration via discrete Fourier transform. According to different beam scanning modes, the subsequent analyses show that the MBA coherent integration algorithm based on SSMB (MBACIA-SSMB) may have a better detection performance than that based on TSMB (MBACIA-TSMB). Moreover, the capabilities to estimate the target’s radial velocity and tangency velocity are analyzed. Finally, some numerical experiments are given to verify the performances of MBACIA-TSMB and MBACIA-SSMB.