  Multi-wavelength observations of pulsar emission properties are powerful
means to constrain their magnetospheric activity and magnetic topology. Usually
a star centred magnetic dipole model is invoked to explain the main
characteristics of this radiation. However in some particular pulsars where
observational constraints exist, such simplified models are unable to predict
salient features of their multi-wavelength emission. This paper aims to
carefully model the radio and X-ray emission of PSR~J1136+1551 with an
off-centred magnetic dipole to reconcile both wavelength measurements. We
simultaneously fit the radio pulse profile with its polarization and the
thermal X-ray emission from the polar cap hot spots of PSR~J1136+1551. We are
able to pin down the parameters of the non-dipolar geometry (which we have
assumed to be an offset dipole) and the viewing angle, meanwhile accounting for
the time lag between X-rays and radio emission. Our model fits the data if the
off-centred magnetic dipole lies about 20\% below the neutron star surface. We
also expect very asymmetric polar cap shapes and sizes, implying non antipodal
and non identical thermal emission from the hot spots. We conclude that a
non-dipolar surface magnetic field is an essential feature to explain the
multi-wavelength aspects of PSR~J1136+1551 and other similar pulsars.
