public class MyCustomView extends View {
    private final Paint mBackgroundPaint = new Paint();

    // ...

    private void init() {
        mBackgroundPaint.setColor(Color.BLUE);
        mBackgroundPaint.setAntiAlias(true);  // ★アンチエイリアス有効化
    }

    @Override
    protected void onDraw(Canvas canvas) {
        super.onDraw(canvas);

        int w = canvas.getWidth();
        int h = canvas.getHeight();
        int radius = w < h ? w/2 : h/2;
        canvas.drawCircle(w / 2, h / 2, radius, mBackgroundPaint);  // アンチエイリアス有効にした円を描画
    }
}