In this paper we present a valuation model of callable convertible bonds with call notice periods in a setting of optimal stopping problem between the issuer (firm) and the holder (investor). The convertible bond holder can convert the bond into the underlying stock at any time. On the other hand, when the issuer wants to call (s)he must give an advance notice of calling the bond after a certain period. We analyze the pricing of callable convertible bonds with call notice periods. Furthermore, we explore the analytical properties of optimal conversion and call notice boundaries by the holder and the issuer, respectively. The value of convertible bonds and the optimal critical prices are examined numerically by using the finite difference method.