Laser Doppler vibrometry (LDV) is a well known technique to measure the motions, vibrations and mode shapes of structures and machine components. Photodetector-based LDV can only offer a point-wise measurement. However, it is possible to scan the laser beam to build up a vibrometric image. These scanning laser Doppler vibrometers (SLDV) assume that the measurement conditions remain invariant while multiple and identical, sequential measurements are performed. This assumption makes SLDVs impractical to do measurement on transient events. In this paper, we introduce a new method of generating multiple laser beams with different frequency shifts. The laser beams are projected on different points, and the reflected beams interfere with a common reference beam. The cross-talk among object beams can be bypassed with a proper selection of frequency shifts. A simultaneous vibration measurement on multiple points is realized using a single photodetector. Based on the proposed spatial-encoding technology, a self-synchronized prototype of fiber-based multipoint laser Doppler vibrometer at 1550nm wavelength is developed. An addition red pilot laser is used for aiming purpose. It has the flexibility to measure the vibration of different points on various surfaces. The prototype is used to measure the vibration of different points on a cantilever beam and a plate. The measured results match well with simulation results using finite element method (FEM).