Aims. We present 11 high-precision photometric transit observations of the transiting super-Earth planet GJ 1214 b. Combining these data with observations from other authors, we investigate the ephemeris for possible signs of transit timing variations (TTVs) using a Bayesian approach. Methods. The observations were obtained using telescope-defocusing techinques, and achieve a high precision with random errors in the photometry as low as 1 mmag per point. To investigate the possiblity of TTVs in the light curve, we calculate the overall probability of a TTV signal using Bayesian methods. Results. The observations are used to determine the photometric parameters and the physical properties of the GJ 1214 system. Our results are in good agreement with published values. Individual times of mid-transit are measured with uncertainites as low as 10 s, allowing us to reduce the uncertainity in the orbital period by a factor or two. Conclusions. A Bayesian analysis reveals that it is highly improbable that the observed transit times is explained by TTV caused by a planet in the nominal habitable zone, when compared with the simpler alternative of a linear ephemeris.