Synthetic research of eco-hydrological process in Heihe River Basin (HRB) is a hot spot of research in recent years in arid and semi-arid areas of China. Response of eco-hydraulic processes to climate change is an important scientific issue. Based on the monitoring records of air temperature, humidity and precipitation of HRB from May 1956 to June 2015, together with data of eight global climate indices, periodicities of the above time series and teleconnections between meteorological elements and climate indices were investigated by wavelet analysis. The results show that: (1) The teleconnections between air temperature and climate indices are fine, while the teleconnections between humidity, precipitation and climate indices are comparatively weaker. Significant teleconnections between air temperature and NIN03.4 SSTA, SOI,NAO, AO, WP, PNA, PDO are identified. (2) Teleconnections between air temperature of midstream and downstream of HRB and NIN03.4 SSTA, SOI is on periodicity of 12-16 a;teleconnection between air temperature of upstream and midstream of HRB and NAO is on periodicity of 8-13 a; teleconnection between air temperature of midstream and downstream of HRB and AO is on periodicity of 8-11 a; teleconnection between air temperature and WP is on periodicity of 5-9 a; tele-connection between air temperature of downstream of HRB and PNA is on periodicity of 7-11 a; teleconnection between air temperature of midstream and downstream of HRB and PDO is on periodicity of 11-15 a; while the periodicities of upstream are 2-4 a and 8-14 a. (3) Significant teleconnections between humidity and NAO, POL, WP are identified. Teleconnection between humidity and NAO is on periodicity of 4-5 a; teleconnection between humidity and POL is on periodicity of 3-6 a; teleconnection between humidity of midstream and downstream of HRB and WP is on periodicity of 9-15 a; and humidity delay is about 2-4 a. (4) Significant teleconnections between precipitation and NIN03.4 SSTA,NAO,AO, POL,WP are identified. Teleconnection between precipitation of midstream and downstream of HRB and NIN03.4 SSTA is on periodicity of 9-15 a; teleconnection between precipitation and NAO is on periodicity of 2-4 a; teleconnection between precipitation of upstream of HRB and AO is on periodicity of 3-7 a; teleconnection between precipitation of midstream and downstream of HRB and POL is on periodicity of 11-19 a; while the teleconnection of upstream is on periodicity of 4-6 a; teleconnection between precipitation of midstream of HRB and WP is on periodicity of 9-14 a. This is the first time that systematic analysis of teleconnections between meteorological elements and climate indices at a large basin scale was carried out in China. Findings and methods presented here help understand the response of basin meteorological elements to climate indices, and expand the knowledge and usable toolbox of approaches that can be used by managers and scientists to improve eco-hydraulic processes and water resource planning and operations under future climate uncertainty.