The low-lying structure of Zr-94(40) was studied with the (n, n' gamma) reaction, and a level scheme was established based on excitation function and gamma gamma coincidence measurements. Branching ratios, multipole mixing ratios, and spin assignments were determined from angular distribution measurements. Lifetimes of levels up to 3.4 MeV were measured by the Doppler-shift attenuation method, and for many transitions the reduced transition probabilities were determined. In addition to the anomalous 2(2)(+) state, which has a larger B(E2; 2(2)(+) -> 0(1)(+)) value than the B(E2; 2(1)(+) -> 0(1)(+)), the experimental results revealed interesting and unusual properties of the low-lying states in Zr-94. In a simple interpretation, the excited states are classified in two distinct categories, i.e., those populating the 2(2)(+) state and those decaying to the 2(1)(+) state.