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In this paper we study observational constraints on early dark energy model proposed by Doran & Robbers and growth index using the latest Union2 type Ia supernovae (SNe Ia), the baryon acoustic oscillations (BAO) in the large-scale correlation function of the Sloan Digital Sky Survey and Two-degree Field Galaxy Redshift Survey, cosmic microwave background (CMB) from the Wilkinson Microwave Anisotropy Probe seven-year data, the linear growth factors data and gamma-ray bursts (GRBs). By using the χ² statics method, we constrain the early dark energy model and growth factor from the above datasets. When including the GRB data, we use the cosmographic parameters to calibrate the GRB luminosity relations using SNe Ia. At 2σ confidence level, we find that the fractional dark energy density at early times is Ω_d^e<0.05 using SNe Ia, CMB and BAO. When we include high-redshift probes, such as measurements of the linear growth factors and GRBs, the constraint is tightened considerably and becomes Ω_d^e<0.03 at 2σ confidence level. We also discuss the growth rate index γ. We find γ=0.661_–0.203^+0.302 (1σ) using the SNe Ia, CMB, BAO and linear growth factor data. After including high-redshift GRB data, the growth index is γ=0.653_–0.363^+0.372.