A procedure is proposed for the experimental determination of the spin-parity of the new particle X(3410). It consists of choosing the events representing the radiative decay ψ→X(3410) +γ from the ψ-production experiment at s1/2 = 6.84 GeV, and measuring the angular distribution of the y photon produced in the process, and also the energy distribution of two pseudo-scalar mesons from the subsequent decay of X. The result of calculation shows that the spin-parity of X(3410) can be determined with certainty and good sensitivity.