Transit timing analysis may be an effective method of discovering additional bodies in extrasolar systems which harbour transiting exoplanets. The deviations from the Keplerian motion, caused by mutual gravitational interactions between planets, are expected to generate transit timing variations of transiting exoplanets. In 2009 we collected 9 light curves of 8 transits of the exoplanet WASP-10b. Combining these data with published ones, we found that transit timing cannot be explained by a constant period but by a periodic variation. Simplified three-body models which reproduce the observed variations of timing residuals were identified by numerical simulations. We found that the configuration with an additional planet of mass of $sim$0.1 $M_{rm{J}}$ and orbital period of $sim$5.23 d, located close to the outer 5:3 mean motion resonance, is the most likely scenario. If the second planet is a transiter, the estimated flux drop will be $sim$0.3 per cent and can be observable with a ground-based telescope. Moreover, we present evidence that the spots on the stellar surface and rotation of the star affect the radial velocity curve giving rise to spurious eccentricity of the orbit of the first planet. We argue that the orbit of WASP-10b is essentially circular. Using the gyrochronology method, the host star was found to be $270 pm 80$ Myr old. This young age can explain the large radius reported for WASP-10b.
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