By the theory of localized waves and the vectorial solution of the Maxwell equation, we develop and explore the vector characteristics of the new square Hermite–Gaussian vortex pulsed beam possessing orbital angular momentum (OAM). To investigate the propagation performance of this new beam, the measurement probability model of OAM states for square Hermite–Gaussian vortex pulsed beam propagation through oceanic turbulence is built. We discover through the numerical simulation that a large propagation distance causes a large delay of arrival time for this vortex pulsed beam. Under the same conditions, both the measurement signal probability and the measurement crosstalk probability of OAM states reach the peak at the arrival time. The wide initial half-pulse width and the low OAM quantum number can improve a measurement signal probability and decrease a measurement crosstalk probability of OAM states. Oceanic turbulence with a weak dissipation rate of mean-squared temperature, a small temperature and salinity ratio, a long inner scale and a strong dissipation rate of turbulent kinetic energy has a weak disturbance on the measurement signal probability and a strong disturbance on the measurement crosstalk probability of OAM states for the square Hermite–Gaussian vortex pulsed beam.
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