BVR light curves and radial velocities for the double-lined eclipsing binary V1135 Her were obtained .
The brighter component of V1135 Her is a Cepheid variable with a pulsation period of 4.22433 \pm 0.00026 days .
The orbital period of the system is about 39.99782 \pm 0.00233 days , which is the shortest value among the known Type II Cepheid binaries .
The observed B , V , and R magnitudes were cleaned for the intrinsic variations of the primary star .
The remaining light curves , consisting of eclipses and proximity effects , are obtained .
Our analyses of the multi-colour light curves and radial velocities led to the determination of fundamental stellar properties of both components of the interesting system V1135 Her .
The system consists of two evolved stars , G1+K3 between giants and supergiants , with masses of M _ { 1 } =1.461 \pm 0.054 M _ { \odot } and M _ { 2 } =0.504 \pm 0.040 M _ { \odot } and radii of R _ { 1 } =27.1 \pm 0.4 R _ { \odot } and R _ { 2 } =10.4 \pm 0.2 R _ { \odot } .
The pulsating star is almost filling its corresponding Roche lobe which indicates the possibility of mass loss or transfer having taken place .
We find an average distance of d=7500 \pm 450 pc using the BVR magnitudes and also the V-band extinction .
Location in the Galaxy and the distance to the galactic plane with an amount of 1300 pc indicate that it probably belongs to the thick-disk population .
Most of the observed and calculated parameters of the V1135 Her and its location on the color-magnitude and period-luminosity diagrams lead to a classification of an Anomalous Cepheid .