Time-to-collision (TTC) can be used to design the forward collision warning system (FCWS). Conventional TTC is defined as the relative distance divided by the relative velocity. It might result in estimation errors for maneuvers with non-zero relative accelerations. In order to improve the accuracy of TTC estimation, we consider the relative acceleration and extend the region of interest for FCWS from the main lane to adjacent lanes. If we assume constant relative acceleration within the sample time, the relative distance can be approximated using a second order polynomial. Recursive least square technique is employed to estimate associated coefficients. Variable forgetting factor adjusted using relative acceleration is proposed to enhance the approximation accuracies. Similar process is applied to estimate the coefficients of a second order polynomial for the relative polar angle. The estimated coefficients of the second order polynomial of the relative distance can be transformed into the relative distance, relative velocity, and relative acceleration for calculating TTC. If the relative velocity vector is pointing toward the host vehicle, different levels of collision warning are issued according to the TTC values. If the relative velocity vector is not pointing toward the host vehicle, it is determined to be a safe condition even with TTC below the threshold value. A prototype vehicle equipped with a lidar and necessary sensors is used to collect the road test data. Experimental results show that the proposed algorithm can issue valid warnings to the driver without false alarms for the three tests of ISO 15623.