We present ALMA Cycle-0 observations of the CO (6-5) line emission (rest-frame frequency = 691.473 GHz) and of the 435$mu m$ dust continuum emission in the nuclear region of NGC 34, a local luminous infrared galaxy (LIRG) at a distance of 84 Mpc (1 = 407 pc) which contains a Seyfert 2 active galactic nucleus (AGN) and a nuclear starburst. The CO emission is well resolved by the ALMA beam ($rm 0.26times 0.23$), with an integrated flux of $rm f_{CO~(6-5)} = 1004; (pm 151) ; Jy; km; s^{-1}$. Both the morphology and kinematics of the CO (6-5) emission are rather regular, consistent with a compact rotating disk with a size of 200 pc. A significant emission feature is detected on the red-shifted wing of the line profile at the frequency of the $rm H^{13}CN; (8-7)$ line, with an integrated flux of $rm 17.7 pm 2.1 (random) pm 2.7 (sysmatic); Jy;km; s^{-1}$. However, it cannot be ruled out that the feature is due to an outflow of warm dense gas with a mean velocity of $rm 400; km; s^{-1}$. The continuum is resolved into an elongated configuration, and the observed flux corresponds to a dust mass of $rm M_{dust} = 10^{6.97pm 0.13}; M_{sun}$. An unresolved central core ($rm radius simeq 50; pc$) contributes $28%$ of the continuum flux and $19%$ of the CO (6-5) flux, consistent with insignificant contributions of the AGN to both emissions. Both the CO (6-5) and continuum spatial distributions suggest a very high gas column density ($rm >= 10^4; M_{sun}; pc^{-2}$) in the nuclear region at $rm radius <= 100; pc$.
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