Inspired by the present experimental status of charmed-strange mesons, we perform a systematic study of the charmed-strange meson family in which we calculate the mass spectra of the charmed-strange meson family by taking a screening effect into account in the Godfrey-Isgur model and investigate the corresponding strong decays via the quark pair creation model. These phenomenological analyses of charmed-strange mesons not only shed light on the features of the observed charmed-strange states, but also provide important information on future experimental search for the missing higher radial and orbital excitations in the charmed-strange meson family, which will be a valuable task in LHCb, the forthcoming Belle H, and PANDA. SONG et al. PHYSICAL REVIEW D 91, 054031 (2015)TABLE I. Experimental information of the observed charmed-strange states. State Mass (MeV) [1] Width (MeV) [1] First observation Observed decay modes D, 1968.49 ±0.33 o ; 2112.3 ±0.5 <1.9 D*A 2317) 2317.8 ± 0.6 <3.8 BABAR [3] D+/r° [3] 0,1(2460) 2459.6 ± 0.6 <3.5 CLEO [4] D*+n° [4] 0,1 (2536) 2535.12 ±0.13 0.92 ± 0.05 ITEP, SERP [23] D*+r P3] 0 : 2(2573) 2571.9 ±0.8 16+| ± 3 [24] CLEO [24] D°K+ [24] DtA2632)" 2632.5 ± 1.7 ± 5 .0 [25] < 17 [25] SELEX [25] D°K+ [25] 0*1 (2700) 2688 ± 4 ± 3 [26] 112 ± 7 ± 3 6 [26] BABAR [26] DK [26] 2708 ± 9+1(( [27] 108 ± 23+|f [27] Belle [27] D°K+ [27] 2710 ± 2f)2 [28] 149 ± 7+52 t28] BABAR [28] D^K [28] 2709.2 ± 1.9 ± 4.5 [29] 115.8 ± 7.3 ± 12.1 [29] LHCb [29] DK [29] O[./(2860) 2856.6 ± 1.5 ± 5 .0 [26] 47 ± 7 ± 10 [26] BABAR [26] DK [26] 2862 ± 2±f [28] 48 ± 3 ± 6 [28] BABAR [28] D^K [28] 2866.1 ± 1.0 ±6.3 [29] 69.9 ± 3.2 ± 6.6 [29] LHCb [29] DK [29] 0 ; 3(2860) 2860.5 ± 2.6 ± 2.5 ± 6.0 [30,31] 53 ± 7 ± 4 ± 6 [30,31] LHCb [30,31] D°K~ [30,31] OJi (2860) 2859 ± 12 ± 6 ± 23 [30,31] 159 ± 2 3 ± 2 7 ± 7 2 [30,31] LHCb [30,31] D°K-[30,31] 0.5/(3040) 3044 ± 8l5 30 [28] 239 ± 3 5^2 6 [28]