We have improved the stability and temporal response of the laser speckle strain gauge that detects strain from speckle displacement caused by surface deformation. In the gauge, a narrow laser beam is incident on a diffuse surface, and speckle patterns appearing in the light scattered through the symmetrical angles are detected by a pair of linear image sensors. Speckle displacement is derived by a real-time correlator as the peak of the cross correlation between the current frame and a reference frame of the sensor driven at 1000 frames per second. The reference frame is fixed until the correlation peak becomes lower than a threshold. Using a pair of image sensors, followed by the correlators, and a laser of output power of a few tens of milliwatts, we could measure dynamic strain of polymer films at the frequency between a fraction of hertz and 100 Hz. The resolution of the gauge, which only depends on geometry of the optical system and the sensor pitch, is a few tens of microstrains. The upper limit of the measurement can be extended arbitrarily because small incremental strain is integrated.