Very-long-range attraction extending to a separation close to 300 nm was observed between uncharged mica surfaces that are modified by hydrophobic layers of a polymerized ammonium amphiphile. The force distance profile in pure water is expressed by an exponential function composed of intensity parameter and decay length. Their values determined from the deflection method are 1.7 +/- 0.5 mN/m and 62 +/- 4 nm, respectively. The same parameters obtained from the jump-in method, 0.59 mN/m and 72 nm, agree within the experimental error. This hydrophobic layer is prepared by the Langmuir-Blodgett (LB) deposition in the down-stroke mode (transfer ratio: 0.8) and is stable enough to allow us to study salt effects on the attraction, practically for the first time. The intensity parameter decreases to 0.25 mN/m (from deflection) and 0.18 mN/m (from jump-in) with increasing NaBr concentrations to 10 mM, whereas the decay length remained unchanged at around 60 nm. Interestingly, hydrophobic surfaces prepared by monolayer transfer in the up-stroke mode(transfer ratio: 1.0) display the attraction which extends in pure water to only ca. 30 nm, although their pull-off forces are the same as those for the down-stroke preparations (200-300 mN/m, which corresponds to the interfacial energy of 21-32 mJ/m2). Therefore, the long-range attraction is very sensitive to small structural differences of the hydrophobic surface. The unprecedented long-range attraction cannot be readily accommodated previous explanations which are based on conventional hydration force and cavitation. The concept of ''vicinal water'' by Drost-Hansen can be an alternative basis of the observed attraction. We propose that the structural correlation of interfacial water extend to the submicron range, if the interface is sufficiently large, molecularly smooth, and strongly hydrophobic. The enhanced structural correlation leads to long-range attraction.