Had MRI on brain one year ago. Results normal. Should I still be concerned about a brain tumour?

Almost certainly not. But depends on why you got the MRI in the first place, and whether they did an adequate examination. Most commonly if you were having symptoms like headache, nausea, or other neurologic symptoms and the MRI showed nothing then a hidden brain tumor is unlikely. Rarely, with a poor quality examination a non enhancing tumor can be missed but this is very uncommon.