It's Grade II listed. From the Historic England entry:
HOLLIDAY STREET 1. 5104 Edgbaston B1 Holliday Street Canal Acqueduct SP 08 NE 7/58 II 2. Dated 1870. Cast iron framed acqueduct taking canal from Gas Street Basin over the road. The trough is carried on segmental brick vaults between guiders supported by cross guiders resting on decorated cast iron columns along the pavement edge both sides of the road. The bridge parapets of iron have diamond patterned panels.
Graces Guide also has an entry as follows. Date varies from Historic England entry. 
The present 'Holliday Street Aqueduct' in central Birmingham was constructed in 1884, presumably to replace an existing aqueduct. It is a 42 ft span bridge of considerable width, built to carry the Worcester and Birmingham Canal, and a wharf, road and railway over Holliday Street. One source gives the width as 54.30 m (178 ft)[1], another as 156 ft.
When constructed it carried a wide access road originally leading from Bridge Street to Worcester Wharf (now housing) over Holliday Street, very close to the Worcester Bar stop lock in Gas Street Basin.
The aqueduct has 24 cast iron columns made by Handyside and Co of Derby. These support riveted wrought iron I-beam girders, from which are sprung brick jack arches. The canal has cast iron bed plates. The east end is on a slight curve, demanding a complex arrangement of transverse beams at that end.