  In the N=1 supersymmetric coset minimal model based on (B_N^{(1)} \oplus
D_N^{(1)}, D_N^{(1)}) at level (k,1) studied recently, the standard N=1 super
stress tensor of spins (3/2,2) is reviewed. By considering the stress tensor in
the coset (B_N^{(1)}, D_N^{(1)}) at level k, the higher spin-2' Casimir current
was obtained previously. By acting the above spin-3/2 current on the higher
spin-2' Casimir current, its superpartner, the higher spin-5/2 current, can be
generated and combined as the first higher spin supercurrent with spins (2',
5/2). By calculating the operator product expansions (OPE) between the higher
spin supercurrent and itself, the next higher spin supercurrent can be
generated with spins (7/2,4). Moreover, the other higher spin supercurrent with
spins (4',9/2) can be generated by calculating the OPE between the first higher
spin supercurrent with spins (2', 5/2) and the second higher spin supercurrent
with spins (7/2,4). Finally, the higher spin supercurrent, (11/2,6), can be
extracted from the right hand side of OPE between the higher spin
supercurrents, (2', 5/2) and (4', 9/2).
