A laser interferometer with highly linear transfer characteristics for the undistorted measurement of mechanical vibrations is described. The linear transfer behavior is derived by a control loop which holds the optical phase difference within the interferometer on a constant value. As a phase-shifting element we use a linearized PZT actuator with integrated displacement sensor. With this interferometer harmonic and nonhannonic vibrations can be measured over 5 decades in the range of 1 Å to 25 μm. The frequency range extends from really DC to about 10 kHz (-3dB limiting frequency). Within the control loop we use primarily a proportional-integral controller with an integrated Wien-Robinson band-rejection filter which suppresses the resonance frequency of the PZT-actuator. This allows to increase the limiting frequency of the closed-loop interferometer by a factor 3 in contrast to a control loop without a rejection filter.