  We prove that on one K\"{a}hler-Einstein Fano manifold without holomorphic
vector fields, there exists a unique conical K\"{a}hler-Einstein metric along a
simple normal crossing divisor with admissible prescribed cone angles. We also
establish a curvature estimate for conic metrics along a simple normal crossing
divisor which generalizes Li-Rubinstein's estimate and derive high order
estimates from this estimate.
