This paper reports a new model for strained quantum well lasers, which are based on the quantum well transmission line modeling method where effects of both carrier transport and carrier heating have been included. We have applied this new model and studied the effect of carrier transport on the output waveform of a strained quantum well laser both in time and frequency domains. It has been found that the carrier transport increases the turn-on, turn-off delay times and damping of the quantum well laser transient response. Also, analysis in the frequency domain indicates that the carrier transport causes the output spectrum of the quantum well laser in steady state to exhibit a redshift which has a narrower bandwidth and lower magnitude. The simulation results of turning-on transients obtained by the proposed model are compared with those obtained by the rate equation laser model. The new model has also been used to study the effects of pump current spikes on the laser output waveforms properties, and it was found that the presence of current spikes causes (i) wavelength blueshift, (ii) larger bandwidth, and (iii) reduces the magnitude and decreases the side-lobe suppression ratio of the laser output spectrum. Analysis in both frequency and time domains confirms that the new proposed model can accurately predict the temporal and spectral behaviors of strained quantum well lasers.