The carbon-oxygen white dwarf (CO WD)+He star channel is thought to be one of the promising scenarios that produce young type Ia supernovae (SNe Ia). Previous studies found that if the mass-accretion rate is greater than a critical value, the He-accreting CO WD will undergo inwardly propagating (off-centre) carbon ignition when it increases its mass close to the Chandrasekhar limit. Previous works supposed that the inwardly propagating carbon flame would reach the centre, leading to the production of an oxygen-neon (ONe) WD that may collapse into a neutron star but not an SN Ia. However, it is still uncertain how the carbon flame propagates under the effect of mixing mechanisms. In the present work, we aim to investigate the off-centre carbon burning of He-accreting COWDs by considering the effect of convective mixing. We found that the temperature of the flame is high enough to burn the carbon into silicon-group elements in the outer part of the CO core even if convective overshooting is considered, but the flame would quench somewhere inside the WD, resulting in the formation of a C-O-Si WD. Owing to the inefficiency of thermohaline mixing, the C-O-Si WD may explode as an SN Ia if it continues to grow in mass. Our radiation transfer simulations show that SN ejecta with silicon-rich outer layers will form high-velocity absorption lines in Si II, leading to some similarities to a class of high-velocity SNe Ia in spectral evolution. We estimate that the birthrate of SNe Ia with Si-rich envelopes is similar to 1 x 10(-4) yr(-1) in our Galaxy.