Polarizations of the prompt J/psi's produced in the e(+)e(-) annihilation at CLEO energy (root s = 10.58 GeV) are considered in the framework of the nonrelativistic quantum chromodynamics (NRQCD) factorization formalism. We find that the J/psi polarization has a strong dependence on the production mechanism. At CLEO energy, the most dominant J/psi, production mechanism throughout most of phase space is the color-singlet mechanism, e(+)e(-) --> J/psi, + gg, for which J/psi's are highly longitudinally polarized. On the other hand, the dominant J/psi production mechanism at the upper endpoint of the J/psi energy distribution is the color-octet process, e(+)e(-) --> (c (c) over bar)((8)) + g, for which J/psi's are almost unpolarized. Thus, the measurement of the polarization of the endpoint J/psi's is another test of the color-octet mechanism and a constraint on the NRQCD matrix elements.