Accented text-to-speech (TTS) synthesis seeks to generate speech with an accent (L2) as a variant of the standard version (L1). Accented TTS synthesis is challenging as L2 is different from L1 in both in terms of phonetic rendering and prosody pattern. Furthermore, there is no easy solution to the control of the accent intensity in an utterance. In this work, we propose a neural TTS architecture, that allows us to control the accent and its intensity during inference. This is achieved through three novel mechanisms, 1) an accent variance adaptor to model the complex accent variance with three prosody controlling factors, namely pitch, energy and duration; 2) an accent intensity modeling strategy to quantify the accent intensity; 3) a consistency constraint module to encourage the TTS system to render the expected accent intensity at a fine level. Experiments show that the proposed system attains superior performance to the baseline models in terms of accent rendering and intensity control. To our best knowledge, this is the first study of accented TTS synthesis with explicit intensity control.