The electrode polarisations are different in 2-electrodes cell by comparison to a 2-electrodes cell. When you sweep potential in a 3-electrodes cell, you record the i vs E plot for the redox process occurring at WORK electrode only (thus you can study separately the processes at anode or cathode). . 

When you sweep the voltage in a 2-electrode cell you charge-discharge it in a way that risk to destroy the cell.

Upload details of your work in a doc.file for more explanations (instrument used, coin cell CV, records of your failed sweeps).

Thanks a lot for your kind help. I have briefly summarized our setup and results in the attached file. Actually, we use lithium metal as the anode, and most of the configuration is the same as coin cell except the electrode distance. Thanks again.

Have you read this tutorial or a similar one?

http://www.gamry.com/application-notes/battery-research/testing-lithium-ion-batteries/

I was expecting to see charge-discharge cycles at constant current.. 

What instrument do you use? 

Why I see 5V on your CV?

Are you aware on safety hazards (if you apply too high currents or voltages) ?

We use CHI workstation for CV. There is one image of the result for charge/dishcarge cycle with our 2-electrode system. Actually, we conducted the charge/discharge measurement after we found the absent of redox peaks in CV curve, which means there seems no problem of the electrode. For the one up to 5 V, you can ignore it since most of the time our scanning range is 3-4.6 V, and we have adjusted our scanning rate from 0.02 mV/s to 0.2 mV/s. Thanks.

The low conductivity of your electrolyte is the main reason. What is your electrolyte ?

Thanks a lot for your kind reply. Actually, we use 1M LiPF6 in EC/DMC (1:1 wt.%) as the electrolyte, which is widely used in coin cell. 

(electrolyte) ok. How old is it, in years ?

The electrolyte has been used for only several months. Actually, we have also tried the coin cell with this electrolyte and it works. What I am wondering is that why there is so big difference for charge/discharge (it displays plateau and capacity) and CV (no redox peaks).

ok[1] (only several months).

1. Note : However, zero time starts from the day of the preparation, normally noted on the bottles' label. We mark (handwritten) the opening day, also. Life (and service) time scaling for this electrolyte is a complex issue.

Thanks a lot for your suggestion. We will also try fresh electrolyte later. However, it is still strange to me that the coin cell can work well with the same electrolyte and test condition.

It will be "not strange", if we consider[1,2] the electrodes' distance ratio (dtestCell / dcoinCell) that is 2 orders[1]   or more !

1. Note about approx. distance ratio : dtestCell / dcoinCell  ~  almost ~ 10mm / 0.1mm > 102

2. Note about dcoinCell  ~  0.1mm (when it is inside a typical coin cell)

... it was, also, strange to me (in the 80's).