In this study, the detailed magnetic field structure of the dense protostellar core Barnard 335 (B335) was revealed based on near-infrared polarimetric observations of background stars to measure dichroically polarized light produced by magnetically aligned dust grains in the core. Magnetic fields pervading B335 were mapped using 24 stars after subtracting unrelated ambient polarization components, for the first time revealing that they have an axisymmetrically distorted hourglass-shaped structure toward the protostellar core. On the basis of simple two- and three-dimensional magnetic field modeling, magnetic inclination angles in the plane-of-sky and line-of-sight directions were determined to be $90^{circ} pm 7^{circ}$ and $50^{circ} pm 10^{circ}$, respectively. The total magnetic field strength of B335 was determined to be $30.2 pm 17.7$ $mu {rm G}$. The critical mass of B335, evaluated using both magnetic and thermal/turbulent support against collapse, was determined to be $M_{rm cr} = 3.37 pm 0.94$ ${rm M}_{odot}$, which is identical to the observed core mass of $M_{rm core}=3.67$ M$_{odot}$. We thus concluded that B335 started its contraction from a condition near equilibrium. We found a linear relationship in the polarization versus extinction diagram, up to $A_V sim 15$ mag toward the stars with the greatest obscuration, which verified that our observations and analysis provide an accurate depiction of the core.
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