Increasing the sensitivity of surface plasmon resonance (SPR) sensors is important to enable controlling small concentrations of materials in liquid solutions or for gas sensing. Upon using a 10-15 nm top layer of dielectric film with a high value of the real part ε'of the dielectric function, on top of an SPR sensor in the Kretschmann configuration, the sensitivity is improved by few times. The imaginary part ε"of the top nano layer permittivity needs to be small enough in order to reduce the losses and get sharper dips. The stability of the sensor is also improved because the nano layer is protecting the silver from interacting with the environment. In the near infrared range, the sensitivity is enhanced contrary to the standard SPR mode without top nanolayer. The calculated evanescent field is enhanced near the top layer - analyte interface, thus the enhancement is partially due to this fact and partially due to an increase of the interaction length as a waveguiding effect.