We have carried out 13CO(J=2-1) observations of the active star-forming region N159 West in the LMC with ALMA. We have found that the CO distribution at a sub-pc scale is highly elongated with a small width. These elongated clouds called filaments show straight or curved distributions with a typical width of 0.5-1.0pc and a length of 5-10pc. All the known infrared YSOs are located toward the filaments. We have found broad CO wings of two molecular outflows toward young high-mass stars in N159W-N and N159W-S, whose dynamical timescale is ~10^4 yrs. This is the first discovery of protostellar outflow in external galaxies. For N159W-S which is located toward an intersection of two filaments we set up a hypothesis that the two filaments collided with each other ~10^5 yrs ago and triggered formation of the high-mass star having ~37 Mo. The colliding clouds show significant enhancement in linewidth in the intersection, suggesting excitation of turbulence in the shocked interface layer between them as is consistent with the magneto-hydro-dynamical numerical simulations (Inoue & Fukui 2013). This turbulence increases the mass accretion rate to ~6x10^-4 Mo yr^-1, which is required to overcome the stellar feedback to form the high-mass star.