By introducing a compressive-strained quanternary InGaAsP quantum-wells instead of a conventional ternary InGaAs quantum-wells in 1.55.mu.m DFB-LD, the lasing performances canb e improved and the problems caused by the thickness non-uniformity and the compositional abruptness among the hetero-interpaces canb e relaxed. In this paper, we investigated an iptimum InGaAsP/InGaAsP multiple-quantum-well(MQW) structure as an active layer in a direct-modulated 1.55.mu. DFB-LD from the view point of threshold current, chirping charcteristics, and resonance frequency. The optimum compressive-strained MQW structure was revealed as InGaAsP/InGaAsP structure with strain amount of about 1.2%, number of wells $N_{w}$ of 7, well width $L_{w}$ of 58.agns.. The threshold current density J of 500A/c $m^{2}$, the linewidth enhancement factor a of 1.8, and differential resonance frequency of d $f_{r}$/d(I-I)$^{1}$2/=2GHz/(mA)$^{1}$2/(atI=2 $I_{th}$) were expected in 1.55.mu.m .gamma./4-shifted DFB-LD with the cavity length of 400.mu.m long and kL value of 1.25. These values are considerably improved ones compared to those of 1.55um DFB-LD with InGaAs/InGaAsP MQW which have enhancement factor and the resonance frequence frequency by the detuning of lasing wavelength and gain-peak wavelength. It was found that the linewidth enhancement factor of 20% and differential resonance frequency of 35% without the degradation of the threshold current density could be enhanced in the range of -15nm~-20nm detuning which can be realized by controlling the thickness and Incomposition of InGaAsP well. well.and Incomposition of InGaAsP well. well.