A new method, called Jacobian-Gaussian scheme, has been developed to overcome the challenge of bending angle generation for linear and branched molecules in configurational-bias Monte Carlo. This method is simple, general, fast, and robust which can yield high acceptance rates. Since there are several bending angles in a branched point and their energies are coupled to each other, generating one trial that is acceptable for all energetic terms is a difficult problem. In order to reach reasonable acceptance rates, traditional methods either generate many trials uniformly or use prepared tables to generate trials according to the expected distribution. While the former consumes a considerable amount of simulation time, the later needs a modest amount of memory to store the tabulated distribution information. In contrast, this Jacobian-Gaussian scheme decouples the energetic terms through simple variable transformations and then generates each bending angle according to its Boltzmann distribution. Thus, high acceptance rates can be obtained using only a few trials without requirement for generation and storage of distribution data. This method has been shown to be efficient for various molecular types including propane, 2-methylpropane, 2,2-dimethylpropane, and acetone.